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  <doc>
    <id>634</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2001-04-09</completedDate>
    <publishedDate>2001-04-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Tree-Sparse Convex Programs</title>
    <abstract language="eng">Dynamic stochastic programs are prototypical for optimization problems with an inherent tree structure inducing characteristic sparsity patterns in the KKT systems of interior methods. We propose an integrated modeling and solution approach for such tree-sparse programs. Three closely related natural formulations are theoretically analyzed from a control-theoretic viewpoint and compared to each other. Associated KKT solution algorithms with linear complexity are developed and comparisons to other interior approaches and related problem formulations are discussed.</abstract>
    <identifier type="serial">01-08</identifier>
    <identifier type="opus3-id">635</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6340</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematical Methods of Operations Research 56 (2002) 347-376</enrichment>
    <author>Marc Steinbach</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-08</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convex program</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>tree</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete-time optimal control multistage stochastic program</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>recursive factorization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>local projection</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="15A23">Factorization of matrices</collection>
    <collection role="msc" number="65F50">Sparse matrices</collection>
    <collection role="msc" number="90C06">Large-scale problems</collection>
    <collection role="msc" number="90C15">Stochastic programming</collection>
    <collection role="msc" number="90C25">Convex programming</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="OPTINVEST">OPTINVEST</collection>
    <collection role="projects" number="StochProcCtrl">StochProcCtrl</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/634/ZR-01-08.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/634/ZR-01-08.pdf</file>
  </doc>
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