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<export-example>
  <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>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>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/>
    <publisherPlace/>
    <creatingCorporation/>
    <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>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>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>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>
</export-example>
