<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>24301</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1492</pageFirst>
    <pageLast>1502</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>27</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-08-09</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the convergence of the affine hull of the Chvátal-Gomory closures</title>
    <abstract language="eng">Given an integral polyhedron $P\subseteq\mathbb{R}^n$ and a rational polyhedron $Q\subseteq\mathbb{R}^n$ containing the same integer points as $P$, we investigate how many iterations of the Chvátal--Gomory closure operator have to be performed on $Q$ to obtain a polyhedron contained in the affine hull of $P$. We show that if $P$ contains an integer point in its relative interior, then such a number of iterations can be bounded by a function depending only on $n$. On the other hand, we prove that if $P$ is not full-dimensional and does not contain any integer point in its relative interior, then no finite bound on the number of iterations exists.</abstract>
    <parentTitle language="eng">SIAM journal on discrete mathematics</parentTitle>
    <identifier type="doi">10.1137/120898371</identifier>
    <identifier type="url">https://epubs.siam.org/doi/10.1137/120898371</identifier>
    <identifier type="issn">1095-7146</identifier>
    <identifier type="issn">0895-4801</identifier>
    <enrichment key="BTU">nicht an der BTU erstellt / not created at BTU</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <author>
      <firstName>Gennadiy</firstName>
      <lastName>Averkov</lastName>
    </author>
    <submitter>
      <firstName>Angelika</firstName>
      <lastName>Breu</lastName>
    </submitter>
    <author>
      <firstName>Michelle</firstName>
      <lastName>Conforti</lastName>
    </author>
    <author>
      <firstName>Alberto</firstName>
      <lastName>Del Pia</lastName>
    </author>
    <author>
      <firstName>Marco</firstName>
      <lastName>Di Summa</lastName>
    </author>
    <author>
      <firstName>Yuri</firstName>
      <lastName>Faenza</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>affine hul</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Chvátal–Gomory closure</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Chvátal rank</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cutting plane</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integral polyhe-dron</value>
    </subject>
    <collection role="institutes" number="1302">FG Algorithmische Mathematik</collection>
  </doc>
  <doc>
    <id>24293</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>209</pageFirst>
    <pageLast>215</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>9</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-08-08</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On finitely generated closures in the theory of cutting planes</title>
    <parentTitle language="eng">Discrete optimization</parentTitle>
    <identifier type="doi">10.1016/j.disopt.2012.06.003</identifier>
    <identifier type="url">https://www.sciencedirect.com/science/article/pii/S1572528612000436?via%3Dihub</identifier>
    <identifier type="issn">1572-5286</identifier>
    <enrichment key="BTU">nicht an der BTU erstellt / not created at BTU</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <author>
      <firstName>Gennadiy</firstName>
      <lastName>Averkov</lastName>
    </author>
    <submitter>
      <firstName>Angelika</firstName>
      <lastName>Breu</lastName>
    </submitter>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Chvátal–Gomory closure</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cutting plane</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Max-facet-width</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-integer optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Split closure</value>
    </subject>
    <collection role="institutes" number="1302">FG Algorithmische Mathematik</collection>
  </doc>
</export-example>
