TWO SELF-ADAPTIVE CQ ALGORITHMS FOR THE SPLIT FEASIBILITY PROBLEM WITH MULTIPLE OUTPUT SETS

The split feasibility problem with multiple output sets is to find a point x* is an element of boolean AND(t)(i=1) C-i such that A(j)x* is an element of Q(j), j = 1, 2, ..., r where C-i subset of H and Q(j) subset of H-j are nonempty, convex, and closed subsets, H and H-j are Hilbert spaces, and A(j) : H -> H-j are linear and bounded operators. In this paper, we present two self-adaptive ball-relaxed CQ algorithms. Under mild conditions, we establish strong convergence and provide numerical experiments to illustrate the effectiveness of the proposed algorithms.