InforLorV4, PascalFrancis, Corpus, bibRecord, 000654

On unions and dominants of polytopes

Identifieur interne : 000654 ( PascalFrancis/Corpus ); précédent : 000653; suivant : 000655

On unions and dominants of polytopes

Auteurs : Egon Balas ; Alexander Bockmayr ; Nicolai Pisaruk ; Laurence Wolsey

Source :

Mathematical programming [ 0025-5610 ] ; 2004.

RBID : Pascal:04-0361453

Descripteurs français

Pascal (Inist)
- Matroïde, Enveloppe convexe, Polyèdre, Polytope, Nombre cardinal, Polymatroïde.

English descriptors

KwdEn :
- Cardinal number, Convex hull, Matroid, Polyhedron, Polymatroid, Polytope.

Abstract

A well-known result on unions of polyhedra in the same space gives an extended formulation in a higher-dimensional space whose projection is the convex hull of the union. Here in contrast we study the unions of polytopes in different spaces, giving a complete description of the convex hull without additional variables. When the underlying polytopes are monotone, the facets are described explicitly, generalizing results of Hong and Hooker on cardinality rules, and an efficient separation algorithm is proposed. These results are based on an explicit representation of the dominant of a polytope, and an algorithm for the separation problem for the dominant. For non-monotone polytopes, both the dominant and the union are characterized. We also give results on the unions of polymatroids both on disjoint ground sets and on the same ground set generalizing results of Conforti and Laurent.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A02	`01`			`@0 MHPGA4`
A03		`1`		`@0 Math. program.`
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A08	`01`	`1`	`ENG`	`@1 On unions and dominants of polytopes`
A11	`01`	`1`		`@1 BALAS (Egon)`
A11	`02`	`1`		`@1 BOCKMAYR (Alexander)`
A11	`03`	`1`		`@1 PISARUK (Nicolai)`
A11	`04`	`1`		`@1 WOLSEY (Laurence)`
A14	`01`			`@1 Graduate School of Industrial Administration, Carnegie-Mellon University @2 Pittsburgh PA 15213 @3 USA @Z 1 aut.`
A14	`02`			`@1 Université Henri Poincaré, LORIA, B.P.239 @2 54506 Vandoeuvre-lès-Nancy @3 FRA @Z 2 aut. @Z 3 aut.`
A14	`03`			`@1 CORE and INMA, University Catholique de Louvain, 34 Voie du Roman Pays @2 Louvain-la-Neuve, 1348 @3 BEL @Z 4 aut.`
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A21				`@1 2004`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 15655 @5 354000116550740020`
A44				`@0 0000 @1 © 2004 INIST-CNRS. All rights reserved.`
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A64	`01`	`1`		`@0 Mathematical programming`
A66	`01`			`@0 DEU`
C01	`01`		`ENG`	@0 A well-known result on unions of polyhedra in the same space gives an extended formulation in a higher-dimensional space whose projection is the convex hull of the union. Here in contrast we study the unions of polytopes in different spaces, giving a complete description of the convex hull without additional variables. When the underlying polytopes are monotone, the facets are described explicitly, generalizing results of Hong and Hooker on cardinality rules, and an efficient separation algorithm is proposed. These results are based on an explicit representation of the dominant of a polytope, and an algorithm for the separation problem for the dominant. For non-monotone polytopes, both the dominant and the union are characterized. We also give results on the unions of polymatroids both on disjoint ground sets and on the same ground set generalizing results of Conforti and Laurent.
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C03	`01`	`X`	`FRE`	`@0 Matroïde @5 01`
C03	`01`	`X`	`ENG`	`@0 Matroid @5 01`
C03	`01`	`X`	`SPA`	`@0 Matroide @5 01`
C03	`02`	`X`	`FRE`	`@0 Enveloppe convexe @5 02`
C03	`02`	`X`	`ENG`	`@0 Convex hull @5 02`
C03	`02`	`X`	`SPA`	`@0 Cápsula convexa @5 02`
C03	`03`	`X`	`FRE`	`@0 Polyèdre @5 03`
C03	`03`	`X`	`ENG`	`@0 Polyhedron @5 03`
C03	`03`	`X`	`SPA`	`@0 Poliedro @5 03`
C03	`04`	`X`	`FRE`	`@0 Polytope @5 04`
C03	`04`	`X`	`ENG`	`@0 Polytope @5 04`
C03	`04`	`X`	`SPA`	`@0 Politope @5 04`
C03	`05`	`X`	`FRE`	`@0 Nombre cardinal @5 05`
C03	`05`	`X`	`ENG`	`@0 Cardinal number @5 05`
C03	`05`	`X`	`SPA`	`@0 Número cardinal @5 05`
C03	`06`	`X`	`FRE`	`@0 Polymatroïde @4 CD @5 96`
C03	`06`	`X`	`ENG`	`@0 Polymatroid @4 CD @5 96`
N21				`@1 208`
N44	`01`			`@1 PSI`
N82				`@1 PSI`

Format Inist (serveur)

NO :	PASCAL 04-0361453 INIST
ET :	On unions and dominants of polytopes
AU :	BALAS (Egon); BOCKMAYR (Alexander); PISARUK (Nicolai); WOLSEY (Laurence)
AF :	Graduate School of Industrial Administration, Carnegie-Mellon University/Pittsburgh PA 15213/Etats-Unis (1 aut.); Université Henri Poincaré, LORIA, B.P.239/54506 Vandoeuvre-lès-Nancy/France (2 aut., 3 aut.); CORE and INMA, University Catholique de Louvain, 34 Voie du Roman Pays/Louvain-la-Neuve, 1348/Belgique (4 aut.)
DT :	Publication en série; Niveau analytique
SO :	Mathematical programming; ISSN 0025-5610; Coden MHPGA4; Allemagne; Da. 2004; Vol. 99; No. 2; Pp. 223-239; Bibl. 17 ref.
LA :	Anglais
EA :	A well-known result on unions of polyhedra in the same space gives an extended formulation in a higher-dimensional space whose projection is the convex hull of the union. Here in contrast we study the unions of polytopes in different spaces, giving a complete description of the convex hull without additional variables. When the underlying polytopes are monotone, the facets are described explicitly, generalizing results of Hong and Hooker on cardinality rules, and an efficient separation algorithm is proposed. These results are based on an explicit representation of the dominant of a polytope, and an algorithm for the separation problem for the dominant. For non-monotone polytopes, both the dominant and the union are characterized. We also give results on the unions of polymatroids both on disjoint ground sets and on the same ground set generalizing results of Conforti and Laurent.
CC :	001D01A03
FD :	Matroïde; Enveloppe convexe; Polyèdre; Polytope; Nombre cardinal; Polymatroïde
ED :	Matroid; Convex hull; Polyhedron; Polytope; Cardinal number; Polymatroid
SD :	Matroide; Cápsula convexa; Poliedro; Politope; Número cardinal
LO :	INIST-15655.354000116550740020
ID :	04-0361453

Links to Exploration step

Pascal:04-0361453

Le document en format XML

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<AF>Graduate School of Industrial Administration, Carnegie-Mellon University/Pittsburgh PA 15213/Etats-Unis (1 aut.); Université Henri Poincaré, LORIA, B.P.239/54506 Vandoeuvre-lès-Nancy/France (2 aut., 3 aut.); CORE and INMA, University Catholique de Louvain, 34 Voie du Roman Pays/Louvain-la-Neuve, 1348/Belgique (4 aut.)</AF>
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On unions and dominants of polytopes

On unions and dominants of polytopes

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