Cut-Generating Functions
Identifieur interne : 005A50 ( Main/Exploration ); précédent : 005A49; suivant : 005A51Cut-Generating Functions
Auteurs : Michele Conforti [Italie] ; Gérard Cornuéjols [États-Unis] ; Aris Daniilidis [Espagne] ; Claude Lemaréchal [France] ; Jérôme Malick [France]Source :
English descriptors
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:
DOI: 10.1007/978-3-642-36694-9_11
Affiliations:
- Espagne, France, Italie, États-Unis
- Auvergne-Rhône-Alpes, Rhône-Alpes, Vénétie
- Grenoble, Padoue
- Université Grenoble-Alpes, Université Joseph Fourier, Université de Grenoble, Université de Padoue
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 000176
- to stream Hal, to step Curation: 000176
- to stream Hal, to step Checkpoint: 000301
- to stream Main, to step Merge: 005D88
- to stream Main, to step Curation: 005A50
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Cut-Generating Functions</title>
<author><name sortKey="Conforti, Michele" sort="Conforti, Michele" uniqKey="Conforti M" first="Michele" last="Conforti">Michele Conforti</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-39512" status="VALID"> <orgName>Department of Pure and Applied Mathematics</orgName>
<orgName type="acronym">UNIPD</orgName>
<desc> <address> <addrLine>Università degli Studi di Padova Dipartimento di Matematica Pura ed Applicata Address: Via Trieste, 63 35121 Padova (Italy)</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.math.unipd.it/</ref>
</desc>
<listRelation> <relation active="#struct-301093" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-301093" type="direct"><org type="institution" xml:id="struct-301093" status="VALID"> <orgName>Universita degli Studi di Padova</orgName>
<desc> <address> <addrLine>Via 8 Febbraio 2, 35122 Padova</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.unipd.it/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Italie</country>
<placeName><settlement type="city">Padoue</settlement>
<region type="region" nuts="2">Vénétie</region>
</placeName>
<orgName type="university">Université de Padoue</orgName>
</affiliation>
</author>
<author><name sortKey="Cornuejols, Gerard" sort="Cornuejols, Gerard" uniqKey="Cornuejols G" first="Gérard" last="Cornuéjols">Gérard Cornuéjols</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-87848" status="VALID"> <orgName>Tepper School of Business</orgName>
<desc> <address> <addrLine>5000 Forbes Ave., Pittsburgh, PA 15213, USA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.tepper.cmu.edu/</ref>
</desc>
<listRelation> <relation active="#struct-67135" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-67135" type="direct"><org type="institution" xml:id="struct-67135" status="VALID"> <orgName>Carnegie Mellon University [Pittsburgh]</orgName>
<orgName type="acronym">CMU</orgName>
<desc> <address> <addrLine>5000 Forbes Ave, Pittsburgh, PA 15213</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.cmu.edu/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Daniilidis, Aris" sort="Daniilidis, Aris" uniqKey="Daniilidis A" first="Aris" last="Daniilidis">Aris Daniilidis</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-73761" status="VALID"> <orgName>Departament de Matemàtiques [Barcelona]</orgName>
<desc> <address> <addrLine>Edifici C Campus de la UAB 08193 Bellaterra (Cerdanyola del Vallès)</addrLine>
<country key="ES"></country>
</address>
<ref type="url">http://www.uab.cat/servlet/Satellite/maths-department-1210142393255.html</ref>
</desc>
<listRelation> <relation active="#struct-98227" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-98227" type="direct"><org type="institution" xml:id="struct-98227" status="VALID"> <orgName>Universitat Autònoma de Barcelona [Barcelona]</orgName>
<orgName type="acronym">UAB</orgName>
<desc> <address> <addrLine>UAB Campus 08193 Bellaterra Barcelona</addrLine>
<country key="ES"></country>
</address>
<ref type="url">http://www.uab.es/english/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Espagne</country>
</affiliation>
</author>
<author><name sortKey="Lemarechal, Claude" sort="Lemarechal, Claude" uniqKey="Lemarechal C" first="Claude" last="Lemaréchal">Claude Lemaréchal</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-44907" status="VALID"> <idno type="RNSR">200418269V</idno>
<orgName>Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems</orgName>
<orgName type="acronym">BIPOP</orgName>
<desc> <address> <addrLine>Inria Grenoble - Rhône-Alpes 655 avenue de l'Europe - Montbonnot 38334 Saint Ismier Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/bipop</ref>
</desc>
<listRelation> <relation active="#struct-2497" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-24474" type="direct"></relation>
<relation active="#struct-3886" type="indirect"></relation>
<relation active="#struct-51016" type="indirect"></relation>
<relation active="#struct-300339" type="indirect"></relation>
<relation name="UMR5224" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-445543" type="indirect"></relation>
<relation active="#struct-300275" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-2497" type="direct"><org type="laboratory" xml:id="struct-2497" status="VALID"> <idno type="RNSR">199218244V</idno>
<orgName>Inria Grenoble - Rhône-Alpes</orgName>
<desc> <address> <addrLine>Inovallée655 avenue de l'Europe38330 Montbonnot</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/grenoble</ref>
</desc>
<listRelation> <relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-24474" type="direct"><org type="laboratory" xml:id="struct-24474" status="VALID"> <idno type="IdRef">184945011</idno>
<idno type="RNSR">200711891Z</idno>
<orgName>Laboratoire Jean Kuntzmann</orgName>
<orgName type="acronym">LJK</orgName>
<date type="start">2007-01-01</date>
<desc> <address> <addrLine>Bâtiment IMAG, CS 40700, F-38058 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://ljk.imag.fr</ref>
</desc>
<listRelation> <relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300339" type="direct"></relation>
<relation name="UMR5224" active="#struct-441569" type="direct"></relation>
<relation active="#struct-445543" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-3886" type="indirect"><org type="institution" xml:id="struct-3886" status="OLD"> <idno type="IdRef">02640432X</idno>
<orgName>Université Pierre Mendès France - Grenoble 2</orgName>
<orgName type="acronym">UPMF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="indirect"><org type="institution" xml:id="struct-51016" status="OLD"> <idno type="IdRef">026404796</idno>
<orgName>Université Joseph Fourier - Grenoble 1</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300339" type="indirect"><org type="institution" xml:id="struct-300339" status="VALID"> <orgName>Institut Polytechnique de Grenoble - Grenoble Institute of Technology</orgName>
<desc> <address> <country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5224" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-445543" type="indirect"><org type="institution" xml:id="struct-445543" status="VALID"><idno type="IdRef">188399275</idno>
<orgName>Université Grenoble Alpes</orgName>
<orgName type="acronym">UGA</orgName>
<date type="start">2016-01-01</date>
<desc><address><addrLine>CS 40700 - 38058 Grenoble cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-grenoble-alpes.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="direct"><org type="institution" xml:id="struct-300275" status="OLD"> <idno type="IdRef">026388804</idno>
<orgName>Institut National Polytechnique de Grenoble </orgName>
<orgName type="acronym">INPG</orgName>
<date type="end">2006-12-31</date>
<desc> <address> <addrLine>46 avenue Félix Viallet 38031 Grenoble Cedex 1</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<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>
<author><name sortKey="Malick, Jerome" sort="Malick, Jerome" uniqKey="Malick J" first="Jérôme" last="Malick">Jérôme Malick</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-44907" status="VALID"> <idno type="RNSR">200418269V</idno>
<orgName>Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems</orgName>
<orgName type="acronym">BIPOP</orgName>
<desc> <address> <addrLine>Inria Grenoble - Rhône-Alpes 655 avenue de l'Europe - Montbonnot 38334 Saint Ismier Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/bipop</ref>
</desc>
<listRelation> <relation active="#struct-2497" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-24474" type="direct"></relation>
<relation active="#struct-3886" type="indirect"></relation>
<relation active="#struct-51016" type="indirect"></relation>
<relation active="#struct-300339" type="indirect"></relation>
<relation name="UMR5224" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-445543" type="indirect"></relation>
<relation active="#struct-300275" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-2497" type="direct"><org type="laboratory" xml:id="struct-2497" status="VALID"> <idno type="RNSR">199218244V</idno>
<orgName>Inria Grenoble - Rhône-Alpes</orgName>
<desc> <address> <addrLine>Inovallée655 avenue de l'Europe38330 Montbonnot</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/grenoble</ref>
</desc>
<listRelation> <relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-24474" type="direct"><org type="laboratory" xml:id="struct-24474" status="VALID"> <idno type="IdRef">184945011</idno>
<idno type="RNSR">200711891Z</idno>
<orgName>Laboratoire Jean Kuntzmann</orgName>
<orgName type="acronym">LJK</orgName>
<date type="start">2007-01-01</date>
<desc> <address> <addrLine>Bâtiment IMAG, CS 40700, F-38058 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://ljk.imag.fr</ref>
</desc>
<listRelation> <relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300339" type="direct"></relation>
<relation name="UMR5224" active="#struct-441569" type="direct"></relation>
<relation active="#struct-445543" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-3886" type="indirect"><org type="institution" xml:id="struct-3886" status="OLD"> <idno type="IdRef">02640432X</idno>
<orgName>Université Pierre Mendès France - Grenoble 2</orgName>
<orgName type="acronym">UPMF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="indirect"><org type="institution" xml:id="struct-51016" status="OLD"> <idno type="IdRef">026404796</idno>
<orgName>Université Joseph Fourier - Grenoble 1</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300339" type="indirect"><org type="institution" xml:id="struct-300339" status="VALID"> <orgName>Institut Polytechnique de Grenoble - Grenoble Institute of Technology</orgName>
<desc> <address> <country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5224" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-445543" type="indirect"><org type="institution" xml:id="struct-445543" status="VALID"><idno type="IdRef">188399275</idno>
<orgName>Université Grenoble Alpes</orgName>
<orgName type="acronym">UGA</orgName>
<date type="start">2016-01-01</date>
<desc><address><addrLine>CS 40700 - 38058 Grenoble cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-grenoble-alpes.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="direct"><org type="institution" xml:id="struct-300275" status="OLD"> <idno type="IdRef">026388804</idno>
<orgName>Institut National Polytechnique de Grenoble </orgName>
<orgName type="acronym">INPG</orgName>
<date type="end">2006-12-31</date>
<desc> <address> <addrLine>46 avenue Félix Viallet 38031 Grenoble Cedex 1</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<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>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-00804175</idno>
<idno type="halId">hal-00804175</idno>
<idno type="halUri">https://hal.archives-ouvertes.fr/hal-00804175</idno>
<idno type="url">https://hal.archives-ouvertes.fr/hal-00804175</idno>
<idno type="doi">10.1007/978-3-642-36694-9_11</idno>
<date when="2013-03-18">2013-03-18</date>
<idno type="wicri:Area/Hal/Corpus">000176</idno>
<idno type="wicri:Area/Hal/Curation">000176</idno>
<idno type="wicri:Area/Hal/Checkpoint">000301</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000301</idno>
<idno type="wicri:Area/Main/Merge">005D88</idno>
<idno type="wicri:Area/Main/Curation">005A50</idno>
<idno type="wicri:Area/Main/Exploration">005A50</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Cut-Generating Functions</title>
<author><name sortKey="Conforti, Michele" sort="Conforti, Michele" uniqKey="Conforti M" first="Michele" last="Conforti">Michele Conforti</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-39512" status="VALID"> <orgName>Department of Pure and Applied Mathematics</orgName>
<orgName type="acronym">UNIPD</orgName>
<desc> <address> <addrLine>Università degli Studi di Padova Dipartimento di Matematica Pura ed Applicata Address: Via Trieste, 63 35121 Padova (Italy)</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.math.unipd.it/</ref>
</desc>
<listRelation> <relation active="#struct-301093" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-301093" type="direct"><org type="institution" xml:id="struct-301093" status="VALID"> <orgName>Universita degli Studi di Padova</orgName>
<desc> <address> <addrLine>Via 8 Febbraio 2, 35122 Padova</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.unipd.it/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Italie</country>
<placeName><settlement type="city">Padoue</settlement>
<region type="region" nuts="2">Vénétie</region>
</placeName>
<orgName type="university">Université de Padoue</orgName>
</affiliation>
</author>
<author><name sortKey="Cornuejols, Gerard" sort="Cornuejols, Gerard" uniqKey="Cornuejols G" first="Gérard" last="Cornuéjols">Gérard Cornuéjols</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-87848" status="VALID"> <orgName>Tepper School of Business</orgName>
<desc> <address> <addrLine>5000 Forbes Ave., Pittsburgh, PA 15213, USA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.tepper.cmu.edu/</ref>
</desc>
<listRelation> <relation active="#struct-67135" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-67135" type="direct"><org type="institution" xml:id="struct-67135" status="VALID"> <orgName>Carnegie Mellon University [Pittsburgh]</orgName>
<orgName type="acronym">CMU</orgName>
<desc> <address> <addrLine>5000 Forbes Ave, Pittsburgh, PA 15213</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.cmu.edu/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Daniilidis, Aris" sort="Daniilidis, Aris" uniqKey="Daniilidis A" first="Aris" last="Daniilidis">Aris Daniilidis</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-73761" status="VALID"> <orgName>Departament de Matemàtiques [Barcelona]</orgName>
<desc> <address> <addrLine>Edifici C Campus de la UAB 08193 Bellaterra (Cerdanyola del Vallès)</addrLine>
<country key="ES"></country>
</address>
<ref type="url">http://www.uab.cat/servlet/Satellite/maths-department-1210142393255.html</ref>
</desc>
<listRelation> <relation active="#struct-98227" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-98227" type="direct"><org type="institution" xml:id="struct-98227" status="VALID"> <orgName>Universitat Autònoma de Barcelona [Barcelona]</orgName>
<orgName type="acronym">UAB</orgName>
<desc> <address> <addrLine>UAB Campus 08193 Bellaterra Barcelona</addrLine>
<country key="ES"></country>
</address>
<ref type="url">http://www.uab.es/english/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Espagne</country>
</affiliation>
</author>
<author><name sortKey="Lemarechal, Claude" sort="Lemarechal, Claude" uniqKey="Lemarechal C" first="Claude" last="Lemaréchal">Claude Lemaréchal</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-44907" status="VALID"> <idno type="RNSR">200418269V</idno>
<orgName>Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems</orgName>
<orgName type="acronym">BIPOP</orgName>
<desc> <address> <addrLine>Inria Grenoble - Rhône-Alpes 655 avenue de l'Europe - Montbonnot 38334 Saint Ismier Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/bipop</ref>
</desc>
<listRelation> <relation active="#struct-2497" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-24474" type="direct"></relation>
<relation active="#struct-3886" type="indirect"></relation>
<relation active="#struct-51016" type="indirect"></relation>
<relation active="#struct-300339" type="indirect"></relation>
<relation name="UMR5224" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-445543" type="indirect"></relation>
<relation active="#struct-300275" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-2497" type="direct"><org type="laboratory" xml:id="struct-2497" status="VALID"> <idno type="RNSR">199218244V</idno>
<orgName>Inria Grenoble - Rhône-Alpes</orgName>
<desc> <address> <addrLine>Inovallée655 avenue de l'Europe38330 Montbonnot</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/grenoble</ref>
</desc>
<listRelation> <relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-24474" type="direct"><org type="laboratory" xml:id="struct-24474" status="VALID"> <idno type="IdRef">184945011</idno>
<idno type="RNSR">200711891Z</idno>
<orgName>Laboratoire Jean Kuntzmann</orgName>
<orgName type="acronym">LJK</orgName>
<date type="start">2007-01-01</date>
<desc> <address> <addrLine>Bâtiment IMAG, CS 40700, F-38058 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://ljk.imag.fr</ref>
</desc>
<listRelation> <relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300339" type="direct"></relation>
<relation name="UMR5224" active="#struct-441569" type="direct"></relation>
<relation active="#struct-445543" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-3886" type="indirect"><org type="institution" xml:id="struct-3886" status="OLD"> <idno type="IdRef">02640432X</idno>
<orgName>Université Pierre Mendès France - Grenoble 2</orgName>
<orgName type="acronym">UPMF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="indirect"><org type="institution" xml:id="struct-51016" status="OLD"> <idno type="IdRef">026404796</idno>
<orgName>Université Joseph Fourier - Grenoble 1</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300339" type="indirect"><org type="institution" xml:id="struct-300339" status="VALID"> <orgName>Institut Polytechnique de Grenoble - Grenoble Institute of Technology</orgName>
<desc> <address> <country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5224" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-445543" type="indirect"><org type="institution" xml:id="struct-445543" status="VALID"><idno type="IdRef">188399275</idno>
<orgName>Université Grenoble Alpes</orgName>
<orgName type="acronym">UGA</orgName>
<date type="start">2016-01-01</date>
<desc><address><addrLine>CS 40700 - 38058 Grenoble cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-grenoble-alpes.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="direct"><org type="institution" xml:id="struct-300275" status="OLD"> <idno type="IdRef">026388804</idno>
<orgName>Institut National Polytechnique de Grenoble </orgName>
<orgName type="acronym">INPG</orgName>
<date type="end">2006-12-31</date>
<desc> <address> <addrLine>46 avenue Félix Viallet 38031 Grenoble Cedex 1</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<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>
<author><name sortKey="Malick, Jerome" sort="Malick, Jerome" uniqKey="Malick J" first="Jérôme" last="Malick">Jérôme Malick</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-44907" status="VALID"> <idno type="RNSR">200418269V</idno>
<orgName>Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems</orgName>
<orgName type="acronym">BIPOP</orgName>
<desc> <address> <addrLine>Inria Grenoble - Rhône-Alpes 655 avenue de l'Europe - Montbonnot 38334 Saint Ismier Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/bipop</ref>
</desc>
<listRelation> <relation active="#struct-2497" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-24474" type="direct"></relation>
<relation active="#struct-3886" type="indirect"></relation>
<relation active="#struct-51016" type="indirect"></relation>
<relation active="#struct-300339" type="indirect"></relation>
<relation name="UMR5224" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-445543" type="indirect"></relation>
<relation active="#struct-300275" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-2497" type="direct"><org type="laboratory" xml:id="struct-2497" status="VALID"> <idno type="RNSR">199218244V</idno>
<orgName>Inria Grenoble - Rhône-Alpes</orgName>
<desc> <address> <addrLine>Inovallée655 avenue de l'Europe38330 Montbonnot</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/grenoble</ref>
</desc>
<listRelation> <relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-24474" type="direct"><org type="laboratory" xml:id="struct-24474" status="VALID"> <idno type="IdRef">184945011</idno>
<idno type="RNSR">200711891Z</idno>
<orgName>Laboratoire Jean Kuntzmann</orgName>
<orgName type="acronym">LJK</orgName>
<date type="start">2007-01-01</date>
<desc> <address> <addrLine>Bâtiment IMAG, CS 40700, F-38058 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://ljk.imag.fr</ref>
</desc>
<listRelation> <relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300339" type="direct"></relation>
<relation name="UMR5224" active="#struct-441569" type="direct"></relation>
<relation active="#struct-445543" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-3886" type="indirect"><org type="institution" xml:id="struct-3886" status="OLD"> <idno type="IdRef">02640432X</idno>
<orgName>Université Pierre Mendès France - Grenoble 2</orgName>
<orgName type="acronym">UPMF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="indirect"><org type="institution" xml:id="struct-51016" status="OLD"> <idno type="IdRef">026404796</idno>
<orgName>Université Joseph Fourier - Grenoble 1</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc> <address> <addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300339" type="indirect"><org type="institution" xml:id="struct-300339" status="VALID"> <orgName>Institut Polytechnique de Grenoble - Grenoble Institute of Technology</orgName>
<desc> <address> <country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5224" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-445543" type="indirect"><org type="institution" xml:id="struct-445543" status="VALID"><idno type="IdRef">188399275</idno>
<orgName>Université Grenoble Alpes</orgName>
<orgName type="acronym">UGA</orgName>
<date type="start">2016-01-01</date>
<desc><address><addrLine>CS 40700 - 38058 Grenoble cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-grenoble-alpes.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="direct"><org type="institution" xml:id="struct-300275" status="OLD"> <idno type="IdRef">026388804</idno>
<orgName>Institut National Polytechnique de Grenoble </orgName>
<orgName type="acronym">INPG</orgName>
<date type="end">2006-12-31</date>
<desc> <address> <addrLine>46 avenue Félix Viallet 38031 Grenoble Cedex 1</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<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">10.1007/978-3-642-36694-9_11</idno>
</biblStruct>
</sourceDesc>
</fileDesc>
<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>
</textClass>
</profileDesc>
</teiHeader>
<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>
</orgName>
</list>
<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>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Amérique/explor/PittsburghV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 005A50 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 005A50 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Amérique |area= PittsburghV1 |flux= Main |étape= Exploration |type= RBID |clé= Hal:hal-00804175 |texte= Cut-Generating Functions }}
![]() | This area was generated with Dilib version V0.6.38. | ![]() |