Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem

Abstract

In this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the split feasibility problem. We also give several numerical examples for illustrating the efficiency and implementation of our algorithm in comparison with existing algorithms in the literature.

An inertial triple-projection algorithm for solving the split feasibility problem

“…Inspired by the CQ algorithm, many other projection methods have been developed for solving the SFP, see, for example, [2,7,9,12,20]. Most of these algorithms use invariable stepsize related to a Lipschitz constant, which is inflexible, and only use the current iterate to obtain the next iterate, which may lead to slow convergence.…”