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  <doc>
    <id>7692</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>2019-11-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Maximal Quadratic-Free Sets</title>
    <abstract language="eng">The intersection cut paradigm is a powerful framework that facilitates&#13;
the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a&#13;
simplicial conic relaxation of S and an S-free set: a convex zone whose&#13;
interior does not intersect S. Ideally, such S-free set would be maximal&#13;
inclusion-wise, as it would generate a deeper cutting plane. However, maximality can be a challenging goal in general. In this work, we show how&#13;
to construct maximal S-free sets when S is defined as a general quadratic&#13;
inequality. Our maximal S-free sets are such that efficient separation of&#13;
a vertex in LP-based approaches to quadratically constrained problems is&#13;
guaranteed. To the best of our knowledge, this work is the first to provide&#13;
maximal quadratic-free sets.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-76922</identifier>
    <author>Felipe Serrano</author>
    <submitter>Felipe Serrano</submitter>
    <author>Gonzalo Muñoz</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-56</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MINLP</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quadratic Optimization</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Cutting planes</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="EnBA-M">EnBA-M</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7692/possible_structure.pdf</file>
  </doc>
  <doc>
    <id>7999</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the implementation and strengthening of intersection cuts for QCQPs</title>
    <abstract language="eng">The generation of strong linear inequalities for QCQPs has been recently tackled by a number of authors using the intersection cut paradigm - a highly studied tool in integer programming whose flexibility has triggered these renewed efforts in non-linear settings. In this work, we consider intersection cuts using the recently proposed construction of maximal quadratic-free sets. Using these sets, we derive closed-form formulas to compute intersection cuts which allow for quick cut-computations by simply plugging-in parameters associated to an arbitrary quadratic inequality being violated by a vertex of an LP relaxation. Additionally, we implement a cut-strengthening procedure that dates back to Glover and evaluate these techniques with extensive computational experiments.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-79994</identifier>
    <identifier type="doi">10.1007/978-3-030-73879-2_10</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SourceTitle">Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021, pp. 134-147, Vol.22, 2021</enrichment>
    <author>Antonia Chmiela</author>
    <submitter>Antonia Chmiela</submitter>
    <author>Gonzalo Muñoz</author>
    <author>Felipe Serrano</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Intersection cuts</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>QCQPs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quadratic-free sets</value>
    </subject>
    <collection role="msc" number="90C20">Quadratic programming</collection>
    <collection role="msc" number="90C26">Nonconvex programming, global optimization</collection>
    <collection role="msc" number="90C30">Nonlinear programming</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="EnBA-M">EnBA-M</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7999/ZIBReport_20-29.pdf</file>
  </doc>
</export-example>
