PittsburghV1, France, Analysis, bibRecord, 000186

Cut-generating functions and S-free sets

Identifieur interne : 000186 ( France/Analysis ); précédent : 000185; suivant : 000187

Cut-generating functions and S-free sets

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

Source :

Mathematics of Operations Research [ 0364-765X ] ; 2014-08.

RBID : Hal:hal-01123860

English descriptors

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

Abstract

We consider the separation problem for sets X that are pre-images of a given set S by a linear mapping. Classical examples occur in integer programming, as well as in other optimization problems such as complementarity. One would like to generate valid inequalities that cut off some point not lying in X, without reference to the linear mapping. To this aim, we introduce a concept: cut-generating functions (cgf) and we develop a formal theory for them, largely based on convex analysis. They are intimately related to S-free sets and we study this relation, disclosing several definitions for minimal cgf's and maximal S-free sets. Our work unifies and puts in perspective a number of existing works on S-free sets; in particular, we show how cgf's recover the celebrated Gomory cuts.

Url:

https://hal.archives-ouvertes.fr/hal-01123860

DOI: 10.1287/moor.2014.0670

Affiliations:

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

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Le document en format XML

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<country>France</country>
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<author><name sortKey="Malick, Jerome" sort="Malick, Jerome" uniqKey="Malick J" first="Jérôme" last="Malick">Jérôme Malick</name>
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          <orgName>Centre National de la Recherche Scientifique</orgName>
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<country>France</country>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Joseph Fourier</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Grenoble-Alpes</orgName>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1287/moor.2014.0670</idno>
<series><title level="j">Mathematics of Operations Research</title>
<idno type="ISSN">0364-765X</idno>
<imprint><date type="datePub">2014-08</date>
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</series>
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<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Convex analysis</term>
<term>Generalized gauges</term>
<term>Integer programming</term>
<term>S-free sets</term>
<term>Separation</term>
</keywords>
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<front><div type="abstract" xml:lang="en">We consider the separation problem for sets X that are pre-images of a given set S by a linear mapping. Classical examples occur in integer programming, as well as in other optimization problems such as complementarity. One would like to generate valid inequalities that cut off some point not lying in X, without reference to the linear mapping. To this aim, we introduce a concept: cut-generating functions (cgf) and we develop a formal theory for them, largely based on convex analysis. They are intimately related to S-free sets and we study this relation, disclosing several definitions for minimal cgf's and maximal S-free sets. Our work unifies and puts in perspective a number of existing works on S-free sets; in particular, we show how cgf's recover the celebrated Gomory cuts.</div>
</front>
</TEI>
<affiliations><list><country><li>Espagne</li>
<li>France</li>
<li>États-Unis</li>
</country>
<region><li>Auvergne-Rhône-Alpes</li>
<li>Rhône-Alpes</li>
</region>
<settlement><li>Grenoble</li>
</settlement>
<orgName><li>Université Grenoble-Alpes</li>
<li>Université Joseph Fourier</li>
<li>Université de Grenoble</li>
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<tree><country name="France"><noRegion><name sortKey="Conforti, Michele" sort="Conforti, Michele" uniqKey="Conforti M" first="Michele" last="Conforti">Michele Conforti</name>
</noRegion>
<name sortKey="Lemarechal, Claude" sort="Lemarechal, Claude" uniqKey="Lemarechal C" first="Claude" last="Lemaréchal">Claude Lemaréchal</name>
<name sortKey="Malick, Jerome" sort="Malick, Jerome" uniqKey="Malick J" first="Jérôme" last="Malick">Jérôme Malick</name>
</country>
<country name="États-Unis"><noRegion><name sortKey="Cornuejols, Gerard" sort="Cornuejols, Gerard" uniqKey="Cornuejols G" first="Gérard" last="Cornuéjols">Gérard Cornuéjols</name>
</noRegion>
</country>
<country name="Espagne"><noRegion><name sortKey="Daniilidis, Aris" sort="Daniilidis, Aris" uniqKey="Daniilidis A" first="Aris" last="Daniilidis">Aris Daniilidis</name>
</noRegion>
</country>
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</affiliations>
</record>

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Cut-generating functions and S-free sets

Cut-generating functions and S-free sets

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