Tropical linear-fractional programming and parametric mean payoff games

详细信息	查看全文 | 推荐本文 |

• 作者：Sté ; phane Gaubert^a ; ¹ ; ^{Stephane.Gaubert@inria.fr} ; Ricardo D. Katz^b ; ^{rkatz@fceia.unr.edu.ar} ; Serge沫 Sergeev^a ; ^{sergiej@gmail.com}
• 关键词：Mean payoff games ; Tropical algebra ; Linear programming ; Linear-fractional programming ; Newton iterations ; Lagrange multipliers ; Optimal strategies
• 刊名：Journal of Symbolic Computation
• 出版年：2012
• 期刊代码：140_07477171
• 类别：cp
• 出版时间：December, 2012
• 卷：47
• 期：12
• 页码：1447-1478
• 文件大小：511 K

摘要

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.