Iterative methods of solving stochastic convex feasibility problems and applications

Dan Butnariu; Alfredo N. Iusem; Regina S. Burachik

doi:10.1023/A:1008795702124

Iterative methods of solving stochastic convex feasibility problems and applications

Dan Butnariu, Alfredo N. Iusem, Regina S. Burachik

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	269-307
Number of pages	39
Journal	Computational Optimization and Applications
Volume	15
Issue number	3
DOIs	https://doi.org/10.1023/A:1008795702124
State	Published - 2000

Bibliographical note

Funding Information:
The work of Dan Butnariu was partially done during his visit to the Institute of Pure and Applied Mathematics (IMPA) of Rio de Janeiro, Brazil. Also, Dan Butnariu gratefully acknowledges the support of the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

Access to Document

10.1023/A:1008795702124

Cite this

@article{5b78b558e22143f39bad2d95ffd13afc,

title = "Iterative methods of solving stochastic convex feasibility problems and applications",

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.",

author = "Dan Butnariu and Iusem, {Alfredo N.} and Burachik, {Regina S.}",

note = "Funding Information: The work of Dan Butnariu was partially done during his visit to the Institute of Pure and Applied Mathematics (IMPA) of Rio de Janeiro, Brazil. Also, Dan Butnariu gratefully acknowledges the support of the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.",

year = "2000",

doi = "10.1023/A:1008795702124",

language = "English",

volume = "15",

pages = "269--307",

journal = "Computational Optimization and Applications",

issn = "0926-6003",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - Iterative methods of solving stochastic convex feasibility problems and applications

AU - Butnariu, Dan

AU - Iusem, Alfredo N.

AU - Burachik, Regina S.

N1 - Funding Information: The work of Dan Butnariu was partially done during his visit to the Institute of Pure and Applied Mathematics (IMPA) of Rio de Janeiro, Brazil. Also, Dan Butnariu gratefully acknowledges the support of the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033885848&partnerID=8YFLogxK

U2 - 10.1023/A:1008795702124

DO - 10.1023/A:1008795702124

M3 - Article

AN - SCOPUS:0033885848

SN - 0926-6003

VL - 15

SP - 269

EP - 307

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

IS - 3

ER -

Iterative methods of solving stochastic convex feasibility problems and applications

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this