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    <id>822</id>
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    <completedDate>2004-12-01</completedDate>
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    <title language="eng">The convergence of an interior point method for an elliptic control problem with mixed control-state constraints</title>
    <abstract language="eng">The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples.</abstract>
    <identifier type="serial">04-47</identifier>
    <identifier type="opus3-id">823</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8223</identifier>
    <enrichment key="SourceTitle">Appeared in: Computational Optimization and Applications 39, No. 2 (2008) 183-218</enrichment>
    <author>Uwe Prüfert</author>
    <author>Fredi Tröltzsch</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-47</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>mixed control-state constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Lavrentiev regularization</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49J20">Optimal control problems involving partial differential equations</collection>
    <collection role="msc" number="65M15">Error bounds</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>
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    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
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    <file>https://opus4.kobv.de/opus4-zib/files/822/ZR-04-47.pdf</file>
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    <completedYear>2007</completedYear>
    <publishedYear>2007</publishedYear>
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    <language>eng</language>
    <pageFirst>871</pageFirst>
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    <edition/>
    <issue>6</issue>
    <volume>22</volume>
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    <title language="eng">On two numerical methods for state-constrained elliptic control problems</title>
    <parentTitle language="eng">Optimization Methods and Software</parentTitle>
    <identifier type="url">http://www.math.tu-berlin.de/~pruefert/Publicat/index_en.html</identifier>
    <identifier type="url">/homes/numerik/pruefert/WWW/Publicat/on2numerical.pdf</identifier>
    <author>Christian Meyer</author>
    <author>Uwe Prüfert</author>
    <author>Fredi Tröltzsch</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
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    <language>eng</language>
    <pageFirst>564</pageFirst>
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    <issue>8–9</issue>
    <volume>87</volume>
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    <publisherPlace>Berlin</publisherPlace>
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    <title language="eng">An interior point method for a parabolic optimal control problem with regularized pointwise state constraints</title>
    <parentTitle language="eng">ZAMM</parentTitle>
    <identifier type="doi">10.1002/zamm.200610337</identifier>
    <identifier type="url">http://www.math.tu-berlin.de/~pruefert/Publicat/index_en.html</identifier>
    <author>Uwe Prüfert</author>
    <author>Fredi Tröltzsch</author>
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    <id>2620</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
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    <language>eng</language>
    <pageFirst>183</pageFirst>
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    <issue>2</issue>
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    <title language="eng">The convergence of an interior point method for an elliptic control problem with mixed control-state constraints</title>
    <parentTitle language="eng">Comput. Optim. Appl.</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8223</enrichment>
    <enrichment key="FulltextUrl">http://www.zib.de/weiser/papers/PrTrWs.pdf</enrichment>
    <author>Uwe Prüfert</author>
    <author>Fredi Tröltzsch</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>
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    <id>1908</id>
    <completedYear>2007</completedYear>
    <publishedYear>2007</publishedYear>
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    <language>eng</language>
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    <edition/>
    <issue>SFB-Report 2007-008</issue>
    <volume/>
    <type>other</type>
    <publisherName>SFB Research Center "Mathematical Optimization and Applications in Biomedical Sciences", Karl-Franzens-Universität Graz</publisherName>
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    <title language="eng">POD a-posteriori error estimates for linear-quadratic optimal control problems</title>
    <author>S. Volkwein</author>
    <author>Fredi Tröltzsch</author>
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    <id>1910</id>
    <completedYear>2007</completedYear>
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    <pageFirst>616</pageFirst>
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    <title language="eng">Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints</title>
    <parentTitle language="eng">SIAM Journal on Optimization</parentTitle>
    <identifier type="doi">10.1137/07068240X</identifier>
    <author>E. Casas</author>
    <author>J. de Los Reyes</author>
    <author>Fredi Tröltzsch</author>
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