Iterative methods of solving stochastic convex feasibility problems and applications

Citation
D. Butnariu et al., Iterative methods of solving stochastic convex feasibility problems and applications, COMPUT OP A, 15(3), 2000, pp. 269-307
Citations number
32
Categorie Soggetti
Engineering Mathematics
Journal title
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN journal
09266003 → ACNP
Volume
15
Issue
3
Year of publication
2000
Pages
269 - 307
Database
ISI
SICI code
0926-6003(200003)15:3<269:IMOSSC>2.0.ZU;2-N
Abstract
The stochastic convex feasibility problem (SCFP) is the problem of finding almost common points of measurable families of closed convex subsets in ref lexive and separable Banach spaces. In this paper we prove convergence crit eria for two iterative algorithms devised to solve SCFPs. To do that, we fi rst analyze the concepts of Bregman projection and Bregman function with em phasis on the properties of their local moduli of convexity. The areas of a pplicability of the algorithms we present include optimization problems, li near operator equations, inverse problems, etc., which can be represented a s SCFPs and solved as such. Examples showing how these algorithms can be im plemented are also given.