PittsburghV1, France, Analysis, bibRecord, 000391

Cut-Generating Functions

Identifieur interne : 000391 ( France/Analysis ); précédent : 000390; suivant : 000392

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

Affiliations:

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

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to stream Main, to step Exploration: 005A50
to stream France, to step Extraction: 000391

Links to Exploration step

Hal:hal-00804175

Le document en format XML

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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>
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<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>
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<idno type="DOI">10.1007/978-3-642-36694-9_11</idno>
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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>
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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>
</TEI>
<affiliations><list><country><li>Espagne</li>
<li>France</li>
<li>Italie</li>
<li>États-Unis</li>
</country>
<region><li>Auvergne-Rhône-Alpes</li>
<li>Rhône-Alpes</li>
<li>Vénétie</li>
</region>
<settlement><li>Grenoble</li>
<li>Padoue</li>
</settlement>
<orgName><li>Université Grenoble-Alpes</li>
<li>Université Joseph Fourier</li>
<li>Université de Grenoble</li>
<li>Université de Padoue</li>
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<tree><country name="Italie"><region name="Vénétie"><name sortKey="Conforti, Michele" sort="Conforti, Michele" uniqKey="Conforti M" first="Michele" last="Conforti">Michele Conforti</name>
</region>
</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>
<country name="France"><region name="Auvergne-Rhône-Alpes"><name sortKey="Lemarechal, Claude" sort="Lemarechal, Claude" uniqKey="Lemarechal C" first="Claude" last="Lemaréchal">Claude Lemaréchal</name>
</region>
<name sortKey="Malick, Jerome" sort="Malick, Jerome" uniqKey="Malick J" first="Jérôme" last="Malick">Jérôme Malick</name>
</country>
</tree>
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</record>

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Cut-Generating Functions

Cut-Generating Functions

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