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  <doc>
    <id>1116</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-02-23</completedDate>
    <publishedDate>2009-02-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Consistency Results for the Contact-Stabilized Newmark Method</title>
    <abstract language="eng">The paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Among the numerical integrators, interest focuses on the contact-stabilized Newmark method recently suggested by Deuflhard et al., which is compared to the classical Newmark method and an improved energy dissipative version due to Kane et al. In the absence of contact, any such variant is equivalent to the Störmer-Verlet scheme, which is well-known to have consistency order 2. In the presence of contact, however, the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact. Surprisingly, the question of consistency in the constrained situation has not been solved yet. The present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors. The corresponding estimation of the local discretization error requires the bounded total variation of the solution. The results have consequences for the construction of an adaptive timestep control, which will be worked out subsequently in a forthcoming paper.</abstract>
    <identifier type="serial">09-06</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1165</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11164</identifier>
    <enrichment key="SourceTitle">Appeared under the title "Consistency Results on Newmark Methods for Dynamical Contact Problems" in: Numer. Math., 116/1:65-94 (2010)</enrichment>
    <author>Corinna Klapproth</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Schiela</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-06</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dynamical contact problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>viscoelasticity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Signorini condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>consistency</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newmark method</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="35L85">Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]</collection>
    <collection role="msc" number="74H15">Numerical approximation of solutions</collection>
    <collection role="msc" number="74M15">Contact</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1116/consistency.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1116/consistency.ps</file>
  </doc>
  <doc>
    <id>1156</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-11-18</completedDate>
    <publishedDate>2009-11-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Barrier methods for a control problem from hyperthermia treatment planning</title>
    <abstract language="eng">We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.</abstract>
    <identifier type="serial">09-36</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1215</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11567</identifier>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-36</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyperthermia treatment planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>barrier methods</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49J20">Optimal control problems involving partial differential equations</collection>
    <collection role="msc" number="92C50">Medical applications (general)</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1156/ZR_09_36.pdf</file>
  </doc>
  <doc>
    <id>1100</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-12-10</completedDate>
    <publishedDate>2008-12-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity</title>
    <abstract language="eng">We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.</abstract>
    <identifier type="serial">09-01</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1139</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11007</identifier>
    <enrichment key="SourceTitle">A rev. vers. appeared u. the title "An interior point algorithm with inexact step computation in function space for state constrained optimal control" in: Numerische Mathematik 119(2): 373-407(2011)</enrichment>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <author>Andreas Günther</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptivity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M05">Methods based on necessary conditions</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1100/ZR_09_01.pdf</file>
  </doc>
  <doc>
    <id>1071</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-03-26</completedDate>
    <publishedDate>2008-03-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The minimization of an L^{\infty}-functional subject to an elliptic PDE and state constraints</title>
    <abstract language="eng">We study the optimal control of a maximum-norm objective functional subject to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L^{\infty}-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.</abstract>
    <identifier type="serial">08-17</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1100</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10714</identifier>
    <enrichment key="SourceTitle">Appeared under the title "The Minimization of a maximum-norm functional subject to an elliptic PDE and state constraints" in: Z. angew. Math. Mech., 89(7): 536-551, 2009</enrichment>
    <author>Uwe Prüfert</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-17</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M30">Other methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1071/ZR_08_17.pdf</file>
  </doc>
  <doc>
    <id>1079</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-07-10</completedDate>
    <publishedDate>2008-07-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Perturbation Result for Dynamical Contact Problems</title>
    <abstract language="eng">This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.</abstract>
    <identifier type="serial">08-27</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1113</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10793</identifier>
    <enrichment key="SourceTitle">Appeared in: Numer. Math. Theor. Meth. Appl. 2 (2009)</enrichment>
    <author>Corinna Klapproth</author>
    <submitter>unknown unknown</submitter>
    <author>Peter Deuflhard</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-27</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dynamical contact problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>(visco-)elasticity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Signorini condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newmark method</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="35L85">Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]</collection>
    <collection role="msc" number="74H55">Stability</collection>
    <collection role="msc" number="74M15">Contact</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1079/ZR_08_27.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1079/ZR_08_27.ps</file>
  </doc>
  <doc>
    <id>1101</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-12-10</completedDate>
    <publishedDate>2008-12-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient Constraints</title>
    <abstract language="eng">In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.</abstract>
    <identifier type="serial">08-47</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1138</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11014</identifier>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <author>Winnifried Wollner</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-47</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>necessary optimality conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convergence of the central path</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gradient constrained optimization</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M05">Methods based on necessary conditions</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1101/ZR_08_47.pdf</file>
  </doc>
  <doc>
    <id>1190</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-12-14</completedDate>
    <publishedDate>2010-12-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox</title>
    <abstract language="eng">This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.</abstract>
    <identifier type="serial">10-25</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1253</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11909</identifier>
    <enrichment key="SourceTitle">Appeared in:  A. Dedner  et al. (eds.) Advances in DUNE. Springer, 2012. 101-112</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>unknown unknown</submitter>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-25</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>partial differential equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>generic programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive methods</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65Y99">None of the above, but in this section</collection>
    <collection role="msc" number="68U20">Simulation [See also 65Cxx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1190/ZR_10_25.pdf</file>
  </doc>
  <doc>
    <id>1312</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-06-16</completedDate>
    <publishedDate>2011-06-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Convergence Analysis of Smoothing Methods for Optimal Control of Stationary Variational Inequalities</title>
    <abstract language="eng">In the article an optimal control problem subject to a stationary variational inequality&#13;
is investigated. The optimal control problem is complemented with pointwise control constraints.&#13;
The convergence of a smoothing scheme is analyzed. There, the variational inequality&#13;
is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal&#13;
control problem converge to solutions of the original one. Passing to the limit in the&#13;
optimality system of the regularized problem allows to prove C-stationarity of local solutions of the original problem.&#13;
Moreover, convergence rates with respect to the regularization parameter for the error in the control are obtained.&#13;
These rates coincide with rates obtained by numerical experiments, which are included in the paper.</abstract>
    <identifier type="serial">11-23</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-13125</identifier>
    <author>Anton Schiela</author>
    <submitter>Anton Schiela</submitter>
    <author>Daniel Wachsmuth</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-23</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Variational inequalities</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>control constraints</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>path-following</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>C-stationarity</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1312/ZR-11-23.pdf</file>
  </doc>
  <doc>
    <id>1407</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-09-26</completedDate>
    <publishedDate>2011-09-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the Length of the Primal-Dual Path in Moreau-Yosida-based  Path-following for State Constrained Optimal Control: Analysis and Numerics</title>
    <abstract language="eng">We derive a-priori estimates on the length of the primal-dual path that results from a&#13;
Moreau-Yosida approximation of the feasible set for state constrained optimal control problems. These bounds depend on the regularity of the state and the dimension of the&#13;
problem. Comparison with numerical results indicates that these bounds are sharp and&#13;
are attained for the case of a single active point.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="serial">11-37</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-14071</identifier>
    <author>Anton Schiela</author>
    <submitter>Anton Schiela</submitter>
    <author>Michael Hintermüller</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-37</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>PDE constrained optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>path-following</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1407/ZR-11-37.pdf</file>
  </doc>
  <doc>
    <id>1193</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-12-22</completedDate>
    <publishedDate>2010-12-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Uniqueness criteria for solutions of the adjoint equation in state-constrained optimal control</title>
    <abstract language="eng">The paper considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control&#13;
problems. By a counter-example of Serrin, it is known that, in the presence of&#13;
non-smooth data, a standard weak formulation does not ensure uniqueness for such&#13;
equations. Therefore several notions of solution have been developed that guarantee&#13;
uniqueness. In this note, we compare different definitions of solutions, namely the ones&#13;
of Stampacchia and the two notions of solutions of Casas and Alibert-Raymond, and show that they are the same. As side results, we reformulate the solution&#13;
in the sense of Stampacchia, and prove the existence and uniqueness of solutions in&#13;
in case of mixed boundary conditions.</abstract>
    <identifier type="serial">10-28</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11933</identifier>
    <author>Christian Meyer</author>
    <submitter>-empty- (Opus4 user: admin)</submitter>
    <author>Lucia Panizzi</author>
    <submitter>Anton Schiela</submitter>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-28</number>
    </series>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>elliptic partial differential equations</value>
    </subject>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>measure right hand sides</value>
    </subject>
    <collection role="msc" number="35D99">None of the above, but in this section</collection>
    <collection role="msc" number="46N10">Applications in optimization, convex analysis, mathematical programming, economics</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1193/ZR-10-28.pdf</file>
  </doc>
  <doc>
    <id>1420</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-10-21</completedDate>
    <publishedDate>2011-10-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia</title>
    <abstract language="eng">This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="serial">11-39</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-14204</identifier>
    <enrichment key="SourceTitle">Appeared in: Acta Numerica 21: 307-378, 2012</enrichment>
    <author>Peter Deuflhard</author>
    <submitter>Anton Schiela</submitter>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-39</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyperthermia therapy planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mathematical modelling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Maxwell equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>parameter identification</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="49Mxx">Numerical methods [See also 90Cxx, 65Kxx]</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="65Nxx">Partial differential equations, boundary value problems</collection>
    <collection role="msc" number="92Cxx">Physiological, cellular and medical topics</collection>
    <collection role="msc" number="92C50">Medical applications (general)</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1420/ZR-11-39.pdf</file>
  </doc>
  <doc>
    <id>1474</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-02-24</completedDate>
    <publishedDate>2012-02-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An optimal control problem in polyconvex hyperelasticity</title>
    <abstract language="eng">We consider a shape implant design problem that arises in the context of facial surgery. &#13;
We introduce a reformulation as an optimal control problem, where the control acts&#13;
as a boundary force. The state is modelled as a minimizer of a polyconvex&#13;
hyperelastic energy functional. We show existence of optimal solutions and&#13;
derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results &#13;
are presented.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="serial">12-08</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-14745</identifier>
    <submitter>Lars Lubkoll</submitter>
    <author>Lars Lubkoll</author>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>12-08</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyconvex elasticity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>implant design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <collection role="msc" number="49J20">Optimal control problems involving partial differential equations</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="74B20">Nonlinear elasticity</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="FacialSurgery">FacialSurgery</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1474/ZR-12-08.pdf</file>
  </doc>
  <doc>
    <id>1171</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-06-09</completedDate>
    <publishedDate>2010-06-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Timestep Control for the Contact-Stabilized Newmark Method</title>
    <abstract language="eng">The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.</abstract>
    <identifier type="serial">10-09</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1232</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11714</identifier>
    <enrichment key="SourceTitle">Appeared in: Numerische Mathematik vol. 119 iss. 1 (2011), pp. 49-81</enrichment>
    <author>Corinna Klapproth</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Schiela</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>dynamical contact problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>contact--stabilized Newmark method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>extrapolation methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptivity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>timestep control</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="35L86">Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1171/adaptivity.pdf</file>
  </doc>
  <doc>
    <id>935</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-08-01</completedDate>
    <publishedDate>2006-08-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A continuity result for Nemyckii Operators and some applications in PDE constrained optimal control</title>
    <abstract language="eng">This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same.</abstract>
    <identifier type="serial">06-41</identifier>
    <identifier type="opus3-id">935</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9354</identifier>
    <enrichment key="SourceTitle">A revised version appeared under the title: A Simplified Approach to Semismooth Newton Methods in Function Space in: SIAM J. Optimization, 19(3): 1417-1432, 2008</enrichment>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-41</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>continuity of Nemyckii Operators</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newton methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>second order sufficient conditions</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="46N40">Applications in numerical analysis [See also 65Jxx]</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/935/ZR-06-41.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/935/ZR-06-41.ps</file>
  </doc>
  <doc>
    <id>813</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-09-07</completedDate>
    <publishedDate>2004-09-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Control Reduced Primal Interior Point Method for PDE Constrained Optimization</title>
    <abstract language="eng">A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparable coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples.</abstract>
    <identifier type="serial">04-38</identifier>
    <identifier type="opus3-id">814</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8138</identifier>
    <enrichment key="SourceTitle">Appeared under the title "Control Reduced Primal Interior Point Methods" in: Comp. Optim. and Appl. 41 (2008) pp. 127-145</enrichment>
    <author>Martin Weiser</author>
    <author>Tobias Gänzler</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-38</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discretization error</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="65N15">Error bounds</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/813/ZR-04-38.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/813/ZR-04-38.pdf</file>
  </doc>
  <doc>
    <id>950</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-03-09</completedDate>
    <publishedDate>2007-03-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Barrier Methods for Optimal Control Problems with State Constraints</title>
    <abstract language="eng">We study barrier methods for state constrained optimal control problems with PDEs. In the focus of our analysis is the path of minimizers of the barrier subproblems with the aim to provide a solid theoretical basis for function space oriented path-following algorithms. We establish results on existence, continuity and convergence of this path. Moreover, we consider the structure of barrier subdifferentials, which play the role of dual variables.</abstract>
    <identifier type="serial">07-07</identifier>
    <identifier type="opus3-id">950</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9504</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. on Optimization 20(2): 1002-1031 (2009)</enrichment>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-07</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M05">Methods based on necessary conditions</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/950/ZR-07-07.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/950/ZR-07-07.ps</file>
  </doc>
  <doc>
    <id>909</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-03-27</completedDate>
    <publishedDate>2006-03-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimal Control with State Constraints</title>
    <abstract language="eng">We propose a variant of the control reduced interior point method for the solution of state constrained problems. We show convergence of the corresponding interior point pathfollowing algorithm in function space. Morever, we provide error bounds for the iterates.</abstract>
    <identifier type="serial">06-16</identifier>
    <identifier type="opus3-id">910</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9099</identifier>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-16</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/909/ZR-06-16.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/909/ZR-06-16.ps</file>
  </doc>
  <doc>
    <id>1497</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-04-03</completedDate>
    <publishedDate>2012-04-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A cubic regularization algorithm for nonconvex optimization in function space (in preparation)</title>
    <abstract language="eng">We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization&#13;
problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact &#13;
that in such problems one often has to deal with more than one norm. Global and local convergence results are established&#13;
in a general framework. Moreover, several variants of step computations are compared. In the context of nonlinear &#13;
elasticity it turns out the a cg method applied to an augmented Hessian is more robust than truncated cg.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <author>Anton Schiela</author>
    <submitter>Anton Schiela</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>12-16</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonconvex optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimization in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear elasticity</value>
    </subject>
    <collection role="msc" number="49M37">Methods of nonlinear programming type [See also 90C30, 65Kxx]</collection>
    <collection role="msc" number="74B20">Nonlinear elasticity</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="no-project">no-project</collection>
  </doc>
  <doc>
    <id>2256</id>
    <completedYear>2009</completedYear>
    <publishedYear>2009</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>237</pageFirst>
    <pageLast>257</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>2</volume>
    <type>article</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Perturbation Result for Dynamical Contact Problems</title>
    <parentTitle language="eng">Numer. Math</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-10793</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Corinna Klapproth</author>
    <author>Peter Deuflhard</author>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2379</id>
    <completedYear>2011</completedYear>
    <publishedYear>2011</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>373</pageFirst>
    <pageLast>407</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>119</volume>
    <type>article</type>
    <publisherName>Springer Berlin / Heidelberg</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Interior Point Algorithm with Inexact Step Computation in Function Space for State Constrained Optimal Control</title>
    <parentTitle language="eng">Numer. Math.</parentTitle>
    <identifier type="doi">10.1007/s00211-011-0381-4</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Anton Schiela</author>
    <author>Andreas Günther</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2355</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>369</pageFirst>
    <pageLast>393</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>39</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization</title>
    <parentTitle language="eng">Computational Optimization and Applications</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8490</enrichment>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>2603</id>
    <completedYear>2011</completedYear>
    <publishedYear>2011</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>581</pageFirst>
    <pageLast>600</pageLast>
    <pageNumber>20</pageNumber>
    <edition/>
    <issue>3</issue>
    <volume>48</volume>
    <type>article</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: optimal error estimates and parameter adjustment</title>
    <parentTitle language="eng">Comp. Opt. and Appl.</parentTitle>
    <identifier type="doi">10.1007/s10589-009-9278-x</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-10414</enrichment>
    <author>Michael Hinze</author>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2440</id>
    <completedYear>2007</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>127</pageFirst>
    <pageLast>145</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>41</volume>
    <type>article</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A control reduced primal interior point method for a class of control constrained optimal control problems</title>
    <parentTitle language="eng">Comput. Optim. Appl.</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8138</enrichment>
    <author>Martin Weiser</author>
    <author>Tobias Gänzler</author>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>2444</id>
    <completedYear>2004</completedYear>
    <publishedYear>2004</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>43</pageFirst>
    <pageLast>46</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>4</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Function space interior point methods for PDE constrained optimization</title>
    <parentTitle language="eng">PAMM</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8027</enrichment>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
  </doc>
  <doc>
    <id>2456</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1830</pageFirst>
    <pageLast>1845</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>42</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Asymptotic Mesh Independence of Newton’s Method Revisited</title>
    <parentTitle language="eng">SIAM J. Num. Anal.</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-7352</enrichment>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <author>Peter Deuflhard</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
  </doc>
  <doc>
    <id>2606</id>
    <completedYear>2009</completedYear>
    <publishedYear>2009</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>536</pageFirst>
    <pageLast>551</pageLast>
    <pageNumber/>
    <edition/>
    <issue>7</issue>
    <volume>89</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Minimization of a maximum-norm functional subject to an elliptic PDE and state constraints</title>
    <parentTitle language="eng">Z. angew. Math. Mech.</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-10714</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Uwe Prüfert</author>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2608</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>369</pageFirst>
    <pageLast>393</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>19</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Simplified Approach to Semismooth Newton Methods in Function Space</title>
    <parentTitle language="eng">SIAM J. on Optimization</parentTitle>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2609</id>
    <completedYear>2006</completedYear>
    <publishedYear>2006</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace>Fachbereich Mathematik</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation>FU Berlin</contributingCorporation>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Control Reduced Interior Point Method. A Function Space Oriented Algorithmic Approach</title>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2611</id>
    <completedYear>2009</completedYear>
    <publishedYear>2009</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>70</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Extended Mathematical Framework for Barrier Methods in Function Space</title>
    <parentTitle language="eng">Domain Decomposition Methods in Science and Engineering XVIII</parentTitle>
    <enrichment key="Series">Lecture Notes in Computational Science and Engineering</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-10593</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2613</id>
    <completedYear>2009</completedYear>
    <publishedYear>2009</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1002</pageFirst>
    <pageLast>1031</pageLast>
    <pageNumber>30</pageNumber>
    <edition/>
    <issue>2</issue>
    <volume>20</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Barrier Methods for Optimal Control Problems with State Constraints</title>
    <parentTitle language="eng">SIAM J. on Optimization</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-9504</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>2614</id>
    <completedYear>2009</completedYear>
    <publishedYear>2009</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2407</pageFirst>
    <pageLast>2432</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>48</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">State constrained optimal control problems with states of low regularity</title>
    <parentTitle language="eng">SIAM J. on Control and Optimization</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-509</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Anton Schiela</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
  </doc>
  <doc>
    <id>7703</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>444</pageFirst>
    <pageLast>458</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>81</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-03-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Kaskade 7 - a Flexible Finite Element Toolbox</title>
    <abstract language="eng">Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. &#13;
&#13;
We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.</abstract>
    <parentTitle language="eng">Computers and Mathematics with Applications</parentTitle>
    <identifier type="doi">10.1016/j.camwa.2020.02.011</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-02-11</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-74616</enrichment>
    <submitter>Martin Weiser</submitter>
    <author>Sebastian Götschel</author>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="DFG-RTThermo">DFG-RTThermo</collection>
    <collection role="projects" number="ECMath-CH9">ECMath-CH9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="projects" number="HighPerMeshes">HighPerMeshes</collection>
    <collection role="projects" number="ECMath-CH20">ECMath-CH20</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>7461</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2019-09-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Kaskade 7 -- a Flexible Finite Element Toolbox</title>
    <abstract language="eng">Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the Dune interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. &#13;
&#13;
We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-74616</identifier>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="AcceptedDate">2020-02-11</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-48</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>generic programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>partial differential equations</value>
    </subject>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65Y99">None of the above, but in this section</collection>
    <collection role="msc" number="68U20">Simulation [See also 65Cxx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="DFG-RTThermo">DFG-RTThermo</collection>
    <collection role="projects" number="ECMath-CH9">ECMath-CH9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="projects" number="HighPerMeshes">HighPerMeshes</collection>
    <collection role="projects" number="ECMath-CH20">ECMath-CH20</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7461/ZR19-48.pdf</file>
  </doc>
  <doc>
    <id>50</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-06-17</completedDate>
    <publishedDate>2008-06-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">State constrained optimal control problems with states of low regularity</title>
    <abstract language="eng">We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.</abstract>
    <identifier type="serial">08-24</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1108</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-509</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. on Control and Optimization 48(4): 2407-2432 (2009)</enrichment>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>08-24</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality conditions</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/50/ZR_08_24.pdf</file>
  </doc>
  <doc>
    <id>735</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2003-05-12</completedDate>
    <publishedDate>2003-05-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Asymptotic Mesh Independence of Newton's Method Revisited</title>
    <abstract language="eng">The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.</abstract>
    <identifier type="serial">03-13</identifier>
    <identifier type="opus3-id">736</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7352</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM Journal on Numerical Analysis Vol. 42, No. 5, pp. 1830-1845</enrichment>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh independence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear partial differential equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newton method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>collocation method</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65J15">Equations with nonlinear operators (do not use 65Hxx)</collection>
    <collection role="msc" number="65N22">Solution of discretized equations [See also 65Fxx, 65Hxx]</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/735/ZR-03-13.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/735/ZR-03-13.pdf</file>
  </doc>
  <doc>
    <id>849</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-02-09</completedDate>
    <publishedDate>2005-02-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Superlinear Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization</title>
    <abstract language="eng">A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently proposed method is a primal interior point pathfollowing scheme with the special feature, that the control variable is eliminated from the optimality system. Apart from global linear convergence we show, that this method converges locally almost quadratically, if the optimal solution satisfies a function space analogue to a non-degeneracy condition. In numerical experiments we observe, that a prototype implementation of our method behaves in compliance with our theoretical results.</abstract>
    <identifier type="serial">05-15</identifier>
    <identifier type="opus3-id">849</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8490</identifier>
    <enrichment key="SourceTitle">Appeared in: Comp. Opt. and Appl. 39(3): 369-393, 2008</enrichment>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-15</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>superlinear convergence</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/849/ZR-05-15.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/849/ZR-05-15.ps</file>
  </doc>
  <doc>
    <id>802</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-06-24</completedDate>
    <publishedDate>2004-06-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Function space interior point methods for PDE constrained optimization</title>
    <abstract language="eng">A primal-dual interior point method for optimal control problems with PDE constraints is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed. Numerical results from an inexact continuation method applied to a model problem are shown.</abstract>
    <identifier type="serial">04-27</identifier>
    <identifier type="opus3-id">803</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8027</identifier>
    <enrichment key="SourceTitle">Appeared in : PAMM 4 (1) 43-46 (2004)</enrichment>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-27</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>complementarity functions</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="90C48">Programming in abstract spaces</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/802/ZR-04-27.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/802/ZR-04-27.pdf</file>
  </doc>
  <doc>
    <id>5395</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2015-03-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An affine covariant composite step method for optimization with PDEs as equality constraints</title>
    <abstract language="eng">We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-53954</identifier>
    <enrichment key="SourceTitle">Optimization Methods and Software, DOI 10.1080/10556788.2016.1241783</enrichment>
    <author>Lars Lubkoll</author>
    <submitter> Lubkoll</submitter>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>composite step methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cubic regularization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>affine covariant</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimization with PDEs</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ECMath-CH9">ECMath-CH9</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5395/ZR-15-09.pdf</file>
  </doc>
  <doc>
    <id>5070</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>7</pageFirst>
    <pageLast>25</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>1</volume>
    <type>incollection</type>
    <publisherName>European Mathematical Society</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mathematics cures virtual patients</title>
    <parentTitle language="eng">MATHEON-Mathematics for Key Technologies</parentTitle>
    <enrichment key="Series">Series in Industrial and Applied Mathematics</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <author>Peter Deuflhard</author>
    <submitter>Martin Weiser</submitter>
    <editor>Peter Deuflhard</editor>
    <author>Ralf Kornhuber</author>
    <editor>Martin Grötschel</editor>
    <editor>Dietmar Hömberg</editor>
    <author>Oliver Sander</author>
    <author>Anton Schiela</author>
    <editor>Ulrich Horst</editor>
    <author>Martin Weiser</author>
    <editor>Jürg Kramer</editor>
    <editor>Volker Mehrmann</editor>
    <editor>Konrad Polthier</editor>
    <editor>Frank Schmidt</editor>
    <editor>Christof Schütte</editor>
    <editor>Martin Skutella</editor>
    <editor>Jürgen Sprekels</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>4662</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>307</pageFirst>
    <pageLast>378</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>21</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia</title>
    <abstract language="eng">This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.</abstract>
    <parentTitle language="eng">Acta Numerica</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-14204</enrichment>
    <author>Peter Deuflhard</author>
    <submitter>Martin Weiser</submitter>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>4665</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>101</pageFirst>
    <pageLast>112</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>incollection</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox</title>
    <abstract language="eng">This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.</abstract>
    <parentTitle language="eng">Advances in DUNE</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-11909</enrichment>
    <enrichment key="SourceTitle">Appeared as ZIB-Report</enrichment>
    <author>Sebastian Götschel</author>
    <editor>A. Dedner</editor>
    <submitter>Sebastian Götschel</submitter>
    <author>Martin Weiser</author>
    <editor>B. Flemisch</editor>
    <author>Anton Schiela</author>
    <editor>R. Klöfkorn</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>4646</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1403</pageFirst>
    <pageLast>1422</pageLast>
    <pageNumber>20</pageNumber>
    <edition/>
    <issue>3</issue>
    <volume>52</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An optimal control problem in polyconvex hyperelasticity</title>
    <abstract language="eng">We consider a shape implant design problem that arises in the context of facial surgery. &#13;
 We introduce a reformulation as an optimal control problem, where the control acts&#13;
 as a boundary force. The state is modelled as a minimizer of a polyconvex&#13;
 hyperelastic energy functional. We show existence of optimal solutions and&#13;
 derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results &#13;
 are presented.</abstract>
    <parentTitle language="eng">SIAM J. Control Opt.</parentTitle>
    <identifier type="doi">10.1137/120876629</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-14745</enrichment>
    <author>Lars Lubkoll</author>
    <submitter>Lars Lubkoll</submitter>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="FacialSurgery">FacialSurgery</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>4678</id>
    <completedYear/>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>419</pageFirst>
    <pageLast>428</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>incollection</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Barrier methods for a control problem from hyperthermia treatment planning</title>
    <abstract language="eng">We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.</abstract>
    <parentTitle language="eng">Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009)</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-11567</enrichment>
    <author>Anton Schiela</author>
    <editor>M. Diehl</editor>
    <submitter>Martin Weiser</submitter>
    <author>Martin Weiser</author>
    <editor>F. Glineur</editor>
    <editor>E. Jarlebring</editor>
    <editor>W. Michiels</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>5834</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1132</pageFirst>
    <pageLast>1161</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>32</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An affine covariant composite step method for optimization with PDEs as equality constraints</title>
    <abstract language="eng">We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery.</abstract>
    <parentTitle language="eng">Optimization Methods and Software</parentTitle>
    <identifier type="doi">10.1080/10556788.2016.1241783</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-53954</enrichment>
    <author>Lars Lubkoll</author>
    <submitter>Martin Weiser</submitter>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ECMath-CH9">ECMath-CH9</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
  </doc>
  <doc>
    <id>1041</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-11-27</completedDate>
    <publishedDate>2007-11-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: Optimal Error Estimates and Parameter Adjustment</title>
    <abstract language="eng">An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings.</abstract>
    <identifier type="serial">07-40</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1069</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10414</identifier>
    <enrichment key="SourceTitle">Also: Priority Program 1253, German Research Foundation (DFG), Preprint-Number SPP1253-08-03 (2007)</enrichment>
    <author>Michael Hinze</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Elliptic optimal control problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>error estimates</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pointwise state constraints</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49J20">Optimal control problems involving partial differential equations</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1041/ZR_07_40.pdf</file>
  </doc>
  <doc>
    <id>1047</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-12-13</completedDate>
    <publishedDate>2007-12-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Interior Point Method in Function Space for the Efficient Solution of State Constrained Optimal Control Problems</title>
    <abstract language="eng">We propose and analyse an interior point path-following method in function space for state constrained optimal control. Our emphasis is on proving convergence in function space and on constructing a practical path-following algorithm. In particular, the introduction of a pointwise damping step leads to a very efficient method, as verified by numerical experiments.</abstract>
    <identifier type="serial">07-44</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1076</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10471</identifier>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>07-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M05">Methods based on necessary conditions</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1047/ZR_07_44.pdf</file>
  </doc>
  <doc>
    <id>1034</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-11-15</completedDate>
    <publishedDate>2007-11-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimality Conditions for Convex State Constrained Optimal Control Problems with Discontinuous States</title>
    <abstract language="eng">We discuss first order optimality conditions for state constrained optimal control problems. Our concern is the treatment of problems, where the solution of the state equation is not known to be continuous, as in the case of boundary control in three space dimensions or optimal control with parabolic partial differential equations. We show existence of measure valued Lagrangian multipliers, which have just enough additional regularity to be applicable to all possibly discontinuous solutions of the state equation.</abstract>
    <identifier type="serial">07-35</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1063</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10342</identifier>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>07-35</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality conditions</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1034/fopaper.pdf</file>
  </doc>
  <doc>
    <id>1059</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-02-12</completedDate>
    <publishedDate>2008-02-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Extended Mathematical Framework for Barrier Methods in Function Space</title>
    <abstract language="eng">An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.</abstract>
    <identifier type="serial">08-07</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1088</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10593</identifier>
    <enrichment key="SourceTitle">Appeared in: Domain Decomposition Methods in Science and Engineering XVIII Bercovier, M.; Gander, M.J.; Kornhuber, R.; Widlund, O. (Eds.) 2009. Lecture Notes in Computational Science and Engineering 70, pp 201-208</enrichment>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>08-07</number>
    </series>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1059/ZR_08_07.pdf</file>
  </doc>
  <doc>
    <id>8076</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>A4095</pageFirst>
    <pageLast>A4120</pageLast>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>43</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A primal dual projection algorithm for efficient constraint preconditioning</title>
    <abstract language="eng">We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity.</abstract>
    <parentTitle language="eng">SIAM Journal on Scientific Computing</parentTitle>
    <identifier type="doi">10.1137/20M1380739</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-08-18</enrichment>
    <author>Anton Schiela</author>
    <submitter>Martin Weiser</submitter>
    <author>Matthias Stöcklein</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="projects" number="2020-SPP1962">2020-SPP1962</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>10286</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>173</volume>
    <type>incollection</type>
    <publisherName>Springer Nature</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Identification of Stress in Heterogeneous Contact Models</title>
    <abstract language="eng">We develop a heterogeneous model of the lower limb system to simulate muscle forces and stresses acting on the knee joint. The modelling of the bone dynamics leads to an index-3 DAE, which we discretize by higher order collocation methods. Furthermore, we present an elastomechanical contact knee joint model of the articular cartilage. For the solution of the contact problem we develop an efficient multigrid solver, based on an Augmented-Lagrangian relaxation of the contact constraints. We formulate the identification of joint forces and resulting stresses with respect to different knee joint models as an inverse problem based on&#13;
medical gait data.</abstract>
    <parentTitle language="eng">Non-Smooth and Complementarity-Based Distributed Parameter Systems</parentTitle>
    <subTitle language="deu">Simulation and Hierarchical Optimization, Part II</subTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-03-07</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="Series">International Series of Numerical Mathematics</enrichment>
    <author>Felix Baumann</author>
    <submitter>Martin Weiser</submitter>
    <editor>Michael Hintermüller</editor>
    <author>Georg Duda</author>
    <editor>Roland Herzog</editor>
    <author>Anton Schiela</author>
    <editor>Christian Kanzow</editor>
    <author>Martin Weiser</author>
    <editor>Michael Ulbrich</editor>
    <editor>Stefan Ulbrich</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="persons" number="felix.baumann">Baumann, Felix</collection>
    <collection role="projects" number="2020-SPP1962">2020-SPP1962</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
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