Convex stochastic optimization for random fields on graphs: A method of constructing Lagrange multipliers

I. V. Evstigneev and M. I. Taksar

Mathematical Methods of Operations Research, 2001, vol. 54, issue 2, 217-237

Abstract: The paper analyzes stochastic optimization problems involving random fields on infinite directed graphs. The primary focus is on a problem of maximizing a concave functional of the field subject to a system of convex and linear constraints. The latter are specified in terms of linear operators acting in the space L ∞ . We examine conditions under which these constraints can be relaxed by using dual variables in L 1 – stochastic Lagrange multipliers. We develop a method for constructing the Lagrange multipliers. In contrast to the conventional methods employed for such purposes (relying on the Yosida-Hewitt theorem), our technique is based on an elementary measure-theoretic fact, the “biting lemma”. Copyright Springer-Verlag Berlin Heidelberg 2001

Keywords: Key words: convex stochastic optimization; random fields on countable directed graphs; stochastic Lagrange multipliers; biting lemma; 1991 Mathematics Subject Classification: 90C15; 93E20; 52A41; 90C25; 90A16; 93E99 (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:54:y:2001:i:2:p:217-237

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DOI: 10.1007/s001860100148

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