We study some methods of subgradient projections for solving a convexfeasibility problem with general (not necessarily hyperplanes or half-spaces)convex sets in the inconsistent case and propose a strategy that controls therelaxation parameters in a specific self-adapting manner. This strategy leavesenough user-flexibility but gives a mathematical guarantee for the algorithm'sbehavior in the inconsistent case. We present numerical results ofcomputational experiments that illustrate the computational advantage of thenew method.
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