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  <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/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <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/>
    <publisherPlace/>
    <creatingCorporation/>
    <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>
</export-example>
