On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

Details On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

2008-04-23

arxiv.org/abs/0804.3647v1

SIAM Journal on Optimization 19: 786--807, (2008)

Mathematics

Optimization and Control

SIAM Journal on Optimization, accepted for publication

Scientific paper

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.

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