Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs - CEA - Commissariat à l’énergie atomique et aux énergies alternatives Access content directly
Journal Articles Journal of Mathematical Analysis and Applications Year : 2014

Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs

Abstract

The problem of computing the smallest fixed point of an order-preserving map arises in the study of zero-sum positive stochastic games. It also arises in static analysis of programs by abstract interpretation. In this context, the discount rate may be negative. We characterize the minimality of a fixed point in terms of the nonlinear spectral radius of a certain semidifferential. We apply this characterization to design a policy iteration algorithm, which applies to the case of finite state and action spaces. The algorithm returns a locally minimal fixed point, which turns out to be globally minimal when the discount rate is nonnegative.
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Dates and versions

hal-00940804 , version 1 (11-02-2024)

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Assalé Adjé, Stéphane Gaubert, Eric Goubault. Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs. Journal of Mathematical Analysis and Applications, 2014, 410, pp.227-240. ⟨10.1016/j.jmaa.2013.07.076⟩. ⟨hal-00940804⟩
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