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Steered sequential projections for the inconsistent convex feasibility problem

Yair Censor (yair***at***math.haifa.ac.il)
Alvaro R. De Pierro (alvaro***at***ime.unicamp.br)
Maorun Zaknoon (zaknoon***at***math.haifa.ac.il)

Abstract: We study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step-sizes. This algorithm is applied to the convex feasibility problem by minimizing a proximity function which measures the sum of the Bregman distances to the members of the family of convex sets. The resulting algorithm is a new steered sequential Bregman projection method which generates sequences that converge if they are bounded, regardless of whether the convex feasibility problem is or is not consistent. For orthogonal projections and affine sets the boundedness condition is always fulfilled.

Keywords: Sequential projections, inconsistent convex feasibility problem, steering sequence.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: Nonlinear Analysis: Theory, Methods & Applications (Series A: Theory and Methods), Vol. 59 (2004), pp. 385-405.

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Entry Submitted: 07/18/2004
Entry Accepted: 07/19/2004
Entry Last Modified: 10/04/2004

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