Finitely convergent deterministic and stochastic iterative methods for solving convex feasibility problems |
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Authors: | Kolobov Victor I. Reich Simeon Zalas Rafał |
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Affiliation: | 1.Department of Computer Science, The Technion – Israel Institute of Technology, Haifa, 32000, Israel ;2.Department of Mathematics, The Technion – Israel Institute of Technology, Haifa, 32000, Israel ; |
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Abstract: | We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation parameters form a divergent series. We combine our methods with a very general class of deterministic control sequences where, roughly speaking, we require that sooner or later we encounter a violated constraint if one exists. This requirement is satisfied, in particular, by the cyclic, repetitive and remotest set controls. Moreover, it is almost surely satisfied for random controls. |
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