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  <doc>
    <id>747</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <completedDate>2003-08-13</completedDate>
    <publishedDate>2003-08-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polynomial Inequalities Representing Polyhedra</title>
    <abstract language="eng">Our main result is that every n-dimensional polytope can be described by at most (2n-1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n-2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities.</abstract>
    <identifier type="serial">03-25</identifier>
    <identifier type="opus3-id">748</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7473</identifier>
    <enrichment key="SourceTitle">For a rev. vers. see ZR-04-53; the final version appeared in: Mathematical Programming 103 (2005) 35-44</enrichment>
    <author>Hartwig Bosse</author>
    <author>Martin Grötschel</author>
    <author>Martin Henk</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-25</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedra and polytopes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>semi-algebraic sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral combinatorics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polynomial inequalities</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stability index</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="14P10">Semialgebraic sets and related spaces</collection>
    <collection role="msc" number="52B11">n-dimensional polytopes</collection>
    <collection role="msc" number="52B55">Computational aspects related to convexity (For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx) [See also 68Uxx]</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="msc" number="90C57">Polyhedral combinatorics, branch-and-bound, branch-and-cut</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/747/ZR-03-25.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/747/ZR-03-25.pdf</file>
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