ISSN:
1573-2894
Keywords:
stochastic convex feasibility problem
;
Bregman projection
;
Bregman function
;
modulus of convexity
;
local moduli of convexity
;
very convex function
;
totally convex function
;
regularly convex function
;
Bochner integral
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008795702124
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