Convergence criteria for generalized gradient methods of solving locally Lipschitz feasibility problems

We prove the convergence of a class of iterative algorithms for solving locally Lipschitz feasibility problems, that is, finite systems of inequalities fi(x)≤0, (i ∈ I), where each fi is a locally Lipschitz functional on ℝn. We also obtain a new convergence criterion for the so-called block-iterative projection methods of finding common points of finite families of convex closed subsets of ℝn as defined by Aharoni and Censor ([3]).

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