Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems

Dan Butnariu; Yair Censor; Simeon Reich

doi:10.1023/A:1008654413997

Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems

Dan Butnariu, Yair Censor, Simeon Reich

Department of Mathematics

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

Abstract

The problem considered in this paper is that of finding a point which is common to almost all the members of a measurable family of closed convex subsets of Rⁿ₊₊, provided that such a point exists. The main results show that this problem can be solved by an iterative method essentially based on averaging at each step the Bregman projections with respect to f(x) = ∑ⁿ_i=1 x_i · ln x_ithe current iterate onto the given sets.

Original language	English
Pages (from-to)	21-39
Number of pages	19
Journal	Computational Optimization and Applications
Volume	8
Issue number	1
DOIs	https://doi.org/10.1023/A:1008654413997
State	Published - 1997

Bibliographical note

Funding Information:
The work of Y. Censor was partially supported by the grant HL-28438 at the Medical Image Processing Group (MIPG), Department of Radiology, the University of Pennsylvania, Philadelphia, PA, USA. The work of S. Reich was partially supported by the Fund for the Promotion of Research at the Technion and by the M. and M.L. Bank Mathematics Research Fund at the Technion. The authors are grateful to the referees for their suggestions.

Keywords

Bregman projection
Entropic projection
Modulus of local convexity
Stochastic convex feasibility problem
Very convex function

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

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10.1023/A:1008654413997

Cite this

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title = "Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems",

abstract = "The problem considered in this paper is that of finding a point which is common to almost all the members of a measurable family of closed convex subsets of Rn++, provided that such a point exists. The main results show that this problem can be solved by an iterative method essentially based on averaging at each step the Bregman projections with respect to f(x) = ∑ni=1 xi · ln xithe current iterate onto the given sets.",

keywords = "Bregman projection, Entropic projection, Modulus of local convexity, Stochastic convex feasibility problem, Very convex function",

author = "Dan Butnariu and Yair Censor and Simeon Reich",

note = "Funding Information: The work of Y. Censor was partially supported by the grant HL-28438 at the Medical Image Processing Group (MIPG), Department of Radiology, the University of Pennsylvania, Philadelphia, PA, USA. The work of S. Reich was partially supported by the Fund for the Promotion of Research at the Technion and by the M. and M.L. Bank Mathematics Research Fund at the Technion. The authors are grateful to the referees for their suggestions.",

year = "1997",

doi = "10.1023/A:1008654413997",

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KW - Modulus of local convexity

KW - Stochastic convex feasibility problem

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Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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