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  <doc>
    <id>6624</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>2017-12-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An algorithm based on Semidefinite Programming for finding minimax optimal designs</title>
    <abstract language="eng">An algorithm based on a delayed constraint generation method for solving semi-infinite programs&#13;
for constructing minimax optimal designs for nonlinear models is proposed. The outer optimization level of the minimax&#13;
optimization problem is solved using a semidefinite programming based approach that requires&#13;
the design space be discretized. A nonlinear programming solver is then used to solve the inner program&#13;
to determine the combination of the parameters that yields the worst-case value of the design criterion.&#13;
The proposed algorithm is applied to find minimax optimal designs for  the logistic model, the flexible 4-parameter&#13;
Hill homoscedastic model and the general nth order consecutive reaction model, and shows that it &#13;
(i) produces designs that compare well with minimax $D-$optimal designs obtained from semi-infinite programming method in the literature;&#13;
(ii) can be applied to semidefinite representable optimality criteria, that include the common A-, E-,G-, I- and D-optimality criteria;&#13;
(iii) can tackle design problems with arbitrary linear constraints on the weights; and&#13;
(iv) is fast and relatively easy to use.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.1016/j.csda.2017.09.008</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66249</identifier>
    <enrichment key="SourceTitle">Computational Statistics &amp; Data Analysis</enrichment>
    <author>Belmiro P.M. Duarte</author>
    <submitter>Guillaume Sagnol</submitter>
    <author>Guillaume Sagnol</author>
    <author>Weng Kee Wong</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cutting plane algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Design efficiency</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Equivalence theorem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Model-based optimal design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear programming</value>
    </subject>
    <collection role="msc" number="62K05">Optimal designs</collection>
    <collection role="msc" number="90C47">Minimax problems [See also 49K35]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="sagnol">Sagnol, Guillaume</collection>
    <collection role="projects" number="ZIB-OptDes">ZIB-OptDes</collection>
    <collection role="institutes" number="healthcare">Mathematics of Health Care</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6624/sdp_minmax_ZIB.pdf</file>
  </doc>
</export-example>
