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  <doc>
    <id>1167</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-03-22</completedDate>
    <publishedDate>2010-03-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">State Trajectory Compression for Optimal Control with Parabolic PDEs</title>
    <abstract language="eng">In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.</abstract>
    <identifier type="serial">10-05</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1228</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11676</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Sci. Comp. 34 (1): A161-A184, 2012</enrichment>
    <author>Martin Weiser</author>
    <submitter>unknown unknown</submitter>
    <author>Sebastian Götschel</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-05</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adjoint gradient computation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trajectory storage</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M29">Methods involving duality</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="94A29">Source coding [See also 68P30]</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-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1167/ZR-10-05.pdf</file>
  </doc>
</export-example>
