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

Dan Butnariu (dbutnaru***at***math.haifa.ac.il)
Yair Censor (yair***at***math.haifa.ac.il)
Pini Gurfil (pgurfil***at***technion.ac.il)
Ethan Hadar (ethan.hadar***at***ca.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, Vol. 19 (2008), pp.786-807.

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Entry Submitted: 04/17/2008
Entry Accepted: 05/02/2008
Entry Last Modified: 07/07/2008

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