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arXiv · 0806.1160

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

Assalé Adjé·Stéphane Gaubert·Eric Goubault
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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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Assalé Adjé, Stéphane Gaubert, Eric Goubault. 2008-06-06. Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs. https://doi.org/10.1016/j.jmaa.2013.07.076

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