A constructive fixed point theorem for min-max functions

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In this Subject: <a title="Electrical & Nuclear Engineering" href="/content/subcat?j_subject=187&j_availability=">Electrical & Nuclear Engineering ,&nbsp; <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: Cochet-Terrasson J. ;&nbsp; Gaubert S. ;&nbsp; Gunawardena J.

Authors: Cochet-Terrasson J.; Gaubert S.; Gunawardena J.

Source: Dynamics and Stability of Systems, Volume 14, Number 4, 1 December 1999 , pp. 407-433(27)

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Abstract:

Min-max functions, F :Rⁿ Rⁿ, arise in modelling the dynamic behaviour of discrete event systems. They form a dense subset of those functions which are homogeneous, F_i(x₁ + h, .. . , x_n + h) = Fi(x₁, . . . , x_n) + h, monotonic , x y F(x) F(y), and nonexpansive in the l_infinity norm-so-called topical functions-which have appeared recently in the work of several authors. Our main result characterizes those min-max functions which have a (generalized) fixed point, where Fi(x) = x_i + h for some h R. We deduce several earlier fixed point results. The proof is inspired by Howard's policy improvement scheme in optimal control and yields an algorithm for finding a fixed point, which appears efficient in an important special case. An extended introduction sets the context for this paper in recent work on the dynamics of topical functions.

Language: English

Document Type: Research article

Publication date: 1999-12-01