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  <doc>
    <id>1751</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2829</pageFirst>
    <pageLast>2843</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>439</volume>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-12-20</completedDate>
    <publishedDate>2012-12-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the semidefinite representations of real functions applied to symmetric matrices</title>
    <abstract language="eng">We present a new semidefinite representation for the trace of &#13;
a real function f applied to symmetric matrices, when a&#13;
semidefinite representation of the convex function f is known. Our construction&#13;
is intuitive, and yields a representation that is more compact than the previously known one.&#13;
We also show with the help of matrix geometric means and the Riemannian metric of the set of positive definite matrices&#13;
that for a rational number p in the interval (0,1],&#13;
the matrix X raised to the exponent p is the largest element&#13;
of a set represented by linear matrix inequalities.&#13;
We give numerical results for a problem inspired from the theory&#13;
of experimental designs, which show that the new semidefinite programming formulation&#13;
yields a speed-up factor in the order of 10.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-17511</identifier>
    <identifier type="doi">10.1016/j.laa.2013.08.021</identifier>
    <enrichment key="SourceTitle">Appear in: Linear Algebra and its Applications</enrichment>
    <author>Guillaume Sagnol</author>
    <submitter>Guillaume Sagnol</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>12-50</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>semidefinite representability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal experimental designs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>SDP</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>matrix geometric mean</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="sagnol">Sagnol, Guillaume</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1751/ZR-12-50.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1751/ZR-12-50revised.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1751/sdp_ratpow_zib_final-1.pdf</file>
  </doc>
</export-example>
