Iterative Methods of Solving Stochastic Convex Feasibility Problems andApplications

Authors:
Dan Butnariu;Alfredo N. Iusem;Regina S. Burachik
Affiliations:
Department of Mathematics, University of Haifa, 31905 Haifa, Israel;Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, R.J., CEP 22460-320, Brazil;Departamento de Matemática, Pontifícia Universidade Católica de Rio de Janeiro, Rua Marqués de São Vincente 225, Rio de Janeiro, RJ, CEP 22453-030, Brazil
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

The stochastic convex feasibility problem (SCFP) is theproblem of findingalmost common points of measurable families of closed convex subsets inreflexive and separable Banach spaces. In this paper we prove convergencecriteria for two iterative algorithms devised to solve SCFPs. To do that, wefirst analyze the concepts of Bregman projection and Bregman function withemphasis on the properties of their local moduli of convexity. The areas ofapplicability of the algorithms we present include optimization problems,linear operator equations, inverse problems, etc., which can be representedas SCFPs and solved as such. Examples showing how these algorithms can beimplemented are also given.