On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems

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 that controls the relaxation parameters in a specific manner 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 show the computational advantage of the method.