  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.
