PittsburghV1, Hal, Checkpoint, bibRecord, 000301

Cut-Generating Functions

Identifieur interne : 000301 ( Hal/Checkpoint ); précédent : 000300; suivant : 000302

Cut-Generating Functions

Auteurs : Michele Conforti [Italie] ; Gérard Cornuéjols [États-Unis] ; Aris Daniilidis [Espagne] ; Claude Lemaréchal [France] ; Jérôme Malick [France]

Source :

RBID : Hal:hal-00804175

English descriptors

mix :
- Convex analysis, Generalized gauges, Integer programming, S-free sets, Separation.

Abstract

In optimization problems such as integer programs or their relaxations, one encounters feasible regions that are the inverse images of a specific closed set S by a linear mapping. One would like to generate valid inequalities that cut off infeasible solutions. Formulas for such inequalities can be obtained through cut-generating functions. This paper presents a formal theory of minimal cut-generating functions and maximal S-free sets which is valid independently of the particular S. This theory relies on tools of convex analysis.

Url:

https://hal.archives-ouvertes.fr/hal-00804175

DOI: 10.1007/978-3-642-36694-9_11

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 000176
to stream Hal, to step Curation: 000176

Links to Exploration step

Hal:hal-00804175

Le document en format XML

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<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Convex analysis</term>
<term>Generalized gauges</term>
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<front><div type="abstract" xml:lang="en">In optimization problems such as integer programs or their relaxations, one encounters feasible regions that are the inverse images of a specific closed set S by a linear mapping. One would like to generate valid inequalities that cut off infeasible solutions. Formulas for such inequalities can be obtained through cut-generating functions. This paper presents a formal theory of minimal cut-generating functions and maximal S-free sets which is valid independently of the particular S. This theory relies on tools of convex analysis.</div>
</front>
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<hal api="V3">          <titleStmt>            <title xml:lang="en">Cut-Generating Functions</title>
            <author role="aut">              <persName>                <forename type="first">Michele</forename>
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            <author role="aut">              <persName>                <forename type="first">Gérard</forename>
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            <author role="aut">              <persName>                <forename type="first">Aris</forename>
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            <author role="aut">              <persName>                <forename type="first">Claude</forename>
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              <date type="whenReleased">2013-03-25 12:58:51</date>
              <date type="whenProduced">2013-03-18</date>
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            <idno type="stamp" n="UNIV-GRENOBLE1" p="UGA">Université Joseph Fourier - Grenoble I</idno>
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            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
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                  <email type="domain">inria.fr</email>
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                  <orgName ref="#struct-300009"></orgName>
                  <affiliation ref="#struct-44907"></affiliation>
                </author>
                <author role="aut">                  <persName>                    <forename type="first">Jérôme</forename>
                    <surname>Malick</surname>
                  </persName>
                  <email type="md5">313de414c75c427dd0de1c2aa512aa17</email>
                  <email type="domain">inria.fr</email>
                  <ptr type="url" target="http://bipop.inrialpes.fr/people/malick/"></ptr>
                  <idno type="halauthorid">830542</idno>
                  <orgName ref="#struct-441569"></orgName>
                  <affiliation ref="#struct-44907"></affiliation>
                </author>
              </analytic>
              <monogr>                <idno type="isbn">978-3-642-36693-2</idno>
                <title level="m">Integer Programming and Combinatorial Optimization</title>
                <meeting>                  <title>IPCO 2013 - 16th International Conference on Integer Programming and Combinatorial Optimization</title>
                  <date type="start">2013-03-18</date>
                  <date type="end">2013-03-20</date>
                  <settlement>Valparaíso</settlement>
                  <country key="CL">Chile</country>
                </meeting>
                <editor>Michel Goemans and José Correa</editor>
                <imprint>                  <publisher>Springer</publisher>
                  <biblScope unit="serie">Lecture Notes in Computer Science</biblScope>
                  <biblScope unit="volume">7801</biblScope>
                  <biblScope unit="pp">123-132</biblScope>
                  <date type="datePub">2013</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/978-3-642-36694-9_11</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>            <langUsage>              <language ident="en">English</language>
            </langUsage>
            <textClass>              <keywords scheme="author">                <term xml:lang="en">Integer programming</term>
                <term xml:lang="en">Convex analysis</term>
                <term xml:lang="en">Separation</term>
                <term xml:lang="en">Generalized gauges</term>
                <term xml:lang="en">S-free sets</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halDomain" n="info.info-dm">Computer Science [cs]/Discrete Mathematics [cs.DM]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">In optimization problems such as integer programs or their relaxations, one encounters feasible regions that are the inverse images of a specific closed set S by a linear mapping. One would like to generate valid inequalities that cut off infeasible solutions. Formulas for such inequalities can be obtained through cut-generating functions. This paper presents a formal theory of minimal cut-generating functions and maximal S-free sets which is valid independently of the particular S. This theory relies on tools of convex analysis.</abstract>
          </profileDesc>
        </hal>
</record>

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Cut-Generating Functions

Cut-Generating Functions

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