Iterative methods of solving stochastic convex feasibility problems and applications

The stochastic convex feasibility problem (SCFP) is the problem of finding almost common points of measurable families of closed convex subsets in reflexive and separable Banach spaces. In this paper we prove convergence criteria for two iterative algorithms devised to solve SCFPs. To do that, we first analyze the concepts of Bregman projection and Bregman function with emphasis on the properties of their local moduli of convexity. The areas of applicability of the algorithms we present include optimization problems, linear operator equations, inverse problems, etc., which can be represented as SCFPs and solved as such. Examples showing how these algorithms can be implemented are also given.