An interior points algorithm for the convex feasibility problem |
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Authors: | Ron Aharoni Abraham Berman Yair Censor |
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Institution: | Mathematics Department, Reading University, Reading RG6 2AX, England;Department of Mathematics, Technion-I.I.T., Haifa 32000, Israel;Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31999, Israel |
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Abstract: | The problem of finding a point in the intersection of a finite family of convex sets in the Euclidean space R″ is considered here. We present a general algorithmic scheme which employs projections onto separating hyperplanes instead of projections onto the convex sets. This scheme includes the method of successive projections of Gubin et al., USSR Comp. Math. and Math. Phys. 7 (1967), 1–24, as a special case. A different realization proposed here is capable of handling the problem when the sets are solid and an interior point of each set is available. This alternative algorithm may, in certain cases, be more attractive than the method of Gubin et al. |
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