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    <id>1137</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-07-09</completedDate>
    <publishedDate>2009-07-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Extending a CIP framework to solve MIQCPs</title>
    <abstract language="eng">This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.</abstract>
    <identifier type="serial">09-23</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1186</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11371</identifier>
    <enrichment key="SourceTitle">App. in: Mixed Integer Nonlinear Programming. Jon Lee, Sven Leyffer (eds.) The IMA Volumes in Mathematics and its Applications, 154. Springer 2011, pp. 427-444</enrichment>
    <author>Timo Berthold</author>
    <submitter>unknown unknown</submitter>
    <author>Stefan Heinz</author>
    <author>Stefan Vigerske</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-23</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mixed integer quadratically constrained programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>constraint integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convex relaxation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonconvex</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="90C11">Mixed integer programming</collection>
    <collection role="msc" number="90C20">Quadratic programming</collection>
    <collection role="msc" number="90C26">Nonconvex programming, global optimization</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="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="berthold">Berthold, Timo</collection>
    <collection role="persons" number="heinz">Heinz, Stefan</collection>
    <collection role="persons" number="vigerske">Vigerske, Stefan</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1137/ZR_09_23rev.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1137/ZR_09_23.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1137/ZR_09_23rev.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1137/ZR_09_23.ps</file>
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