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.
Technical report, April 22, 2007. Revised: December 31, 2007. Revised: February 5, 2008. SIAM Journal on Optimization, Vol. 19 (2008), pp.786-807.