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  <doc>
    <id>813</id>
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    <language>eng</language>
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    <edition/>
    <issue/>
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    <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>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
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    <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/>
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    <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>849</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>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/>
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    <type>reportzib</type>
    <publisherName/>
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    <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>
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  <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>
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