Perturbed projections and subgradient projections for the multiple-sets split feasibility problem
Yair Censor (yairmath.haifa.ac.il)
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.
Keywords: Multiple-sets split feasibility; perturbed projections; subgradient projections;
Category 1: Convex and Nonsmooth Optimization
Category 2: Nonlinear Optimization (Unconstrained Optimization )
Citation: Journal of Mathematical Analysis and Applications, Vol. 327, pp. 1244-1256, (2007).
Entry Submitted: 05/16/2006
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