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    <id>7325</id>
    <completedYear/>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2019-05-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley’s Cutting Plane Algorithm</title>
    <abstract language="eng">Recently, Kronqvist et al. (2016) rediscovered the supporting hyperplane algorithm of Veinott (1967) and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by general, not necessarily convex, differentiable functions that satisfy a mild condition.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-73253</identifier>
    <author>Felipe Serrano</author>
    <submitter>Felipe Serrano</submitter>
    <author>Robert Schwarz</author>
    <author>Ambros Gleixner</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-18</number>
    </series>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schwarz">Schwarz, Robert</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/7325/gauge.pdf</file>
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  <doc>
    <id>7840</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>161</pageFirst>
    <pageLast>179</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>78</volume>
    <type>article</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-05-13</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm</title>
    <abstract language="eng">Recently, Kronqvist et al. (J Global Optim 64(2):249–272, 2016) rediscovered the supporting hyperplane algorithm of Veinott (Oper Res 15(1):147–152, 1967) and demonstrated its computational benefits for solving convex mixed integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm (J Soc Ind Appl Math 8(4):703–712, 1960) applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by a class of general, not necessarily convex nor differentiable, functions.</abstract>
    <parentTitle language="eng">Journal of Global Optimization</parentTitle>
    <identifier type="doi">10.1007/s10898-020-00906-y</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-73253</enrichment>
    <author>Felipe Serrano</author>
    <submitter>Felipe Serrano</submitter>
    <author>Robert Schwarz</author>
    <author>Ambros Gleixner</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schwarz">Schwarz, Robert</collection>
    <collection role="projects" number="EnBA-M">EnBA-M</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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