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Perturbed projections and subgradient projections for the multiple-sets split feasibility problem

Yair Censor (yair***at***math.haifa.ac.il)
Avi Motova (avimotova***at***walla.co)
Alexander Segal (asegal***at***math.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).

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Entry Submitted: 05/16/2006
Entry Accepted: 05/16/2006
Entry Last Modified: 01/20/2007

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