Perturbed projections and subgradient projections for the multiple-sets split feasibility problem |
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Authors: | Yair Censor Avi Motova |
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Affiliation: | Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel |
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Abstract: | We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients projections algorithm that generates convergent sequences of iterates in the feasible case. We further derive and analyze a perturbed projection method for the multiple-sets split feasibility problem and, additionally, furnish alternative proofs to two known results. |
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Keywords: | Multiple-sets split feasibility Perturbed projections Subgradient projections CQ-algorithm Averaged operators Proximity function |
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