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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/268627
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/268627
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling 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 Técnicas2025-10-22T12:20:11Zoai: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:34982025-10-22 12:20:12.064CONICET 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
reponame_str CONICET Digital (CONICET)
collection 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
_version_ 1846782646843080704
score 12.982451

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