A splitting-relaxed projection method for solving the split feasibility problem

摘要

The split feasibility problem (SFP) is to find x ∈ C so that Ax ∈ Q, where C is anonempty closed convex subset of Rn, Q is a nonempty closed convex subset of Rm, and A is amatrix from Rn into Rm. One of successful methods for solving the SFP is Byrne’s CQ algorithm.However, to carry out the CQ algorithm, it is required that the closed convex subsets are simpleand that the matrix norm is known in advance. Motivated by Tseng’s splitting method and Yang’srelaxed CQ algorithm, we propose in this paper a new method for solving the SFP, which overcomesthe drawback of the CQ algorithm.