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Perturbed projections and subgradient projections for the multiple-sets split feasibility problem. (English) Zbl 1253.90211

Summary: 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.

MSC:

90C30 Nonlinear programming
65K10 Numerical optimization and variational techniques
90C47 Minimax problems in mathematical programming
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