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    <completedDate>2010-02-08</completedDate>
    <publishedDate>2010-02-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests</title>
    <abstract language="eng">Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system REDUCE. Our long term goal is to integrate REDUCE as a workhorse'' for symbolic computations into a numerical solver.</abstract>
    <identifier type="serial">10-01</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1223</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11644</identifier>
    <enrichment key="SourceTitle">App. in: CASC 2010, Proceedings, Vladimir P. Gerdt (ed.) Springer 2010, LNCS 6244, pp. 205-219</enrichment>
    <author>Winfried Neun</author>
    <submitter>unknown unknown</submitter>
    <author>Thomas Sturm</author>
    <author>Stefan Vigerske</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear Global Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hybrid Symbolic-Numeric Computation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convex Functions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Real Quantifier Elimination</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <collection role="persons" number="vigerske">Vigerske, Stefan</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1164/ZR_10_01.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1164/ZR_10_01.ps</file>
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  <doc>
    <id>4635</id>
    <completedYear/>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>205</pageFirst>
    <pageLast>219</pageLast>
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    <volume>LNCS 6244</volume>
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    <title language="eng">Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests</title>
    <parentTitle language="eng">Computer Algebra in Scientific Computing</parentTitle>
    <identifier type="isbn">978-3-642-15273-3</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-11644</enrichment>
    <author>Winfried Neun</author>
    <submitter> Engel</submitter>
    <author>Thomas Sturm</author>
    <author>Stefan Vigerske</author>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <collection role="persons" number="vigerske">Vigerske, Stefan</collection>
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