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  <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>
</export-example>
