Tropical linear-fractional programming and parametric mean payoff games
- Autores
- Gaubert, Stéphane; Katz, Ricardo David; Sergeev, Serge
- Año de publicación
- 2012
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to study the tropical analogue of the classical linear-fractional programming problem. We construct an associated parametric mean payoff game problem, and show that the optimality of a given point, or the unboundedness of the problem, can be certified by exhibiting a strategy for one of the players having certain infinitesimal properties (involving the value of the game and its derivative) that we characterize combinatorially. We use this idea to design a Newton-like algorithm to solve tropical linear-fractional programming problems, by reduction to a sequence of auxiliary mean payoff game problems.
Fil: Gaubert, Stéphane. École Polytechnique; Francia
Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Sergeev, Serge. École Polytechnique; Francia - Materia
-
MEAN PAYOFF GAMES
TROPICAL ALGEBRA
LINEAR PROGRAMMING
LINEAR-FRACTIONAL PROGRAMMING
NEWTON ITERATIONS
LAGRANGE MULTIPLIERS
OPTIMAL STRATEGIES - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/268627
Ver los metadatos del registro completo
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Tropical linear-fractional programming and parametric mean payoff gamesGaubert, StéphaneKatz, Ricardo DavidSergeev, SergeMEAN PAYOFF GAMESTROPICAL ALGEBRALINEAR PROGRAMMINGLINEAR-FRACTIONAL PROGRAMMINGNEWTON ITERATIONSLAGRANGE MULTIPLIERSOPTIMAL STRATEGIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to study the tropical analogue of the classical linear-fractional programming problem. We construct an associated parametric mean payoff game problem, and show that the optimality of a given point, or the unboundedness of the problem, can be certified by exhibiting a strategy for one of the players having certain infinitesimal properties (involving the value of the game and its derivative) that we characterize combinatorially. We use this idea to design a Newton-like algorithm to solve tropical linear-fractional programming problems, by reduction to a sequence of auxiliary mean payoff game problems.Fil: Gaubert, Stéphane. École Polytechnique; FranciaFil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Sergeev, Serge. École Polytechnique; FranciaAcademic Press Ltd - Elsevier Science Ltd2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/268627Gaubert, Stéphane; Katz, Ricardo David; Sergeev, Serge; Tropical linear-fractional programming and parametric mean payoff games; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 47; 12; 12-2012; 1447-14780747-7171CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717111002525info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2011.12.049info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:46:47Zoai:ri.conicet.gov.ar:11336/268627instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:46:47.964CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Tropical linear-fractional programming and parametric mean payoff games |
title |
Tropical linear-fractional programming and parametric mean payoff games |
spellingShingle |
Tropical linear-fractional programming and parametric mean payoff games Gaubert, Stéphane MEAN PAYOFF GAMES TROPICAL ALGEBRA LINEAR PROGRAMMING LINEAR-FRACTIONAL PROGRAMMING NEWTON ITERATIONS LAGRANGE MULTIPLIERS OPTIMAL STRATEGIES |
title_short |
Tropical linear-fractional programming and parametric mean payoff games |
title_full |
Tropical linear-fractional programming and parametric mean payoff games |
title_fullStr |
Tropical linear-fractional programming and parametric mean payoff games |
title_full_unstemmed |
Tropical linear-fractional programming and parametric mean payoff games |
title_sort |
Tropical linear-fractional programming and parametric mean payoff games |
dc.creator.none.fl_str_mv |
Gaubert, Stéphane Katz, Ricardo David Sergeev, Serge |
author |
Gaubert, Stéphane |
author_facet |
Gaubert, Stéphane Katz, Ricardo David Sergeev, Serge |
author_role |
author |
author2 |
Katz, Ricardo David Sergeev, Serge |
author2_role |
author author |
dc.subject.none.fl_str_mv |
MEAN PAYOFF GAMES TROPICAL ALGEBRA LINEAR PROGRAMMING LINEAR-FRACTIONAL PROGRAMMING NEWTON ITERATIONS LAGRANGE MULTIPLIERS OPTIMAL STRATEGIES |
topic |
MEAN PAYOFF GAMES TROPICAL ALGEBRA LINEAR PROGRAMMING LINEAR-FRACTIONAL PROGRAMMING NEWTON ITERATIONS LAGRANGE MULTIPLIERS OPTIMAL STRATEGIES |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to study the tropical analogue of the classical linear-fractional programming problem. We construct an associated parametric mean payoff game problem, and show that the optimality of a given point, or the unboundedness of the problem, can be certified by exhibiting a strategy for one of the players having certain infinitesimal properties (involving the value of the game and its derivative) that we characterize combinatorially. We use this idea to design a Newton-like algorithm to solve tropical linear-fractional programming problems, by reduction to a sequence of auxiliary mean payoff game problems. Fil: Gaubert, Stéphane. École Polytechnique; Francia Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina Fil: Sergeev, Serge. École Polytechnique; Francia |
description |
Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to study the tropical analogue of the classical linear-fractional programming problem. We construct an associated parametric mean payoff game problem, and show that the optimality of a given point, or the unboundedness of the problem, can be certified by exhibiting a strategy for one of the players having certain infinitesimal properties (involving the value of the game and its derivative) that we characterize combinatorially. We use this idea to design a Newton-like algorithm to solve tropical linear-fractional programming problems, by reduction to a sequence of auxiliary mean payoff game problems. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-12 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/268627 Gaubert, Stéphane; Katz, Ricardo David; Sergeev, Serge; Tropical linear-fractional programming and parametric mean payoff games; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 47; 12; 12-2012; 1447-1478 0747-7171 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/268627 |
identifier_str_mv |
Gaubert, Stéphane; Katz, Ricardo David; Sergeev, Serge; Tropical linear-fractional programming and parametric mean payoff games; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 47; 12; 12-2012; 1447-1478 0747-7171 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717111002525 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2011.12.049 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Academic Press Ltd - Elsevier Science Ltd |
publisher.none.fl_str_mv |
Academic Press Ltd - Elsevier Science Ltd |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.070432 |