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

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

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Article ID: iaor2003798
Country: Germany
Volume: 54
Issue: 2
Start Page Number: 217
End Page Number: 237
Publication Date: Jan 2001
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: ,
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 L1–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’.

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