caa a22 4500 475750659 CHVBK 20180406123522.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1023/A:1008795702124 doi (NATIONALLICENCE)springer-10.1023/A:1008795702124 Iterative Methods of Solving Stochastic Convex Feasibility Problems and Applications [Elektronische Daten] [Dan Butnariu, Alfredo Iusem, Regina Burachik] 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. Kluwer Academic Publishers, 2000 stochastic convex feasibility problem nationallicence Bregman projection nationallicence Bregman function nationallicence modulus of convexity nationallicence local moduli of convexity nationallicence very convex function nationallicence totally convex function nationallicence regularly convex function nationallicence Bochner integral nationallicence Butnariu Dan Department of Mathematics, University of Haifa, 31905, Haifa, Israel aut Iusem Alfredo Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320, Jardim Botânico, Rio de Janeiro, R.J., Brazil aut Burachik Regina Departamento de Matemática, Pontifícia Universidade Católica de Rio de Janeiro, Rua Marqués de São Vincente 225, CEP 22453-030, Rio de Janeiro, RJ, Brazil aut Computational Optimization and Applications Kluwer Academic Publishers 15/3(2000-03-01), 269-307 0926-6003 15:3<269 2000 15 10589 https://doi.org/10.1023/A:1008795702124 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008795702124 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Butnariu Dan Department of Mathematics, University of Haifa, 31905, Haifa, Israel aut NATIONALLICENCE 700 1- Iusem Alfredo Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320, Jardim Botânico, Rio de Janeiro, R.J., Brazil aut NATIONALLICENCE 700 1- Burachik Regina Departamento de Matemática, Pontifícia Universidade Católica de Rio de Janeiro, Rua Marqués de São Vincente 225, CEP 22453-030, Rio de Janeiro, RJ, Brazil aut NATIONALLICENCE 773 0- Computational Optimization and Applications Kluwer Academic Publishers 15/3(2000-03-01), 269-307 0926-6003 15:3<269 2000 15 10589 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer