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On the behavior of subgradient projections methods for convex feasibility problems in Euclidean spaces. (English) Zbl 1161.49033

Summary: 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 the numerical results of computational experiments that illustrate the computational advantage of the new method.

MSC:

49M37 Numerical methods based on nonlinear programming
90C25 Convex programming
49M15 Newton-type methods
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