On the behavior of subgradient projections methods for convex feasibility problems in Euclidean spaces

Dan Butnariu(dbutnarumath.haifa.ac.il)
Yair Censor(yairmath.haifa.ac.il)
Pini Gurfil(pgurfiltechnion.ac.il)
Ethan Hadar(ethan.hadarca.com)

Abstract: We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm's behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method.

Keywords: Subgradient projections, convex feasibility, steering parameters, strategical relaxation.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Technical report, April 22, 2007. Revised: December 31, 2007. Revised: February 5, 2008. SIAM Journal on Optimization, accepted for publication.

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Entry Submitted: 04/17/2008
Entry Accepted: 05/02/2008
Entry Last Modified: 04/17/2008

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