A New CQ Algorithm for Solving Split Feasibility Problems in Hilbert Spaces

Abstract

© 2018, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. In this paper, we propose a CQ-type algorithm for solving the split feasibility problem (SFP) in real Hilbert spaces. The algorithm is designed such that the step-sizes are directly computed at each iteration. We will show that the sequence generated by the proposed algorithm converges in norm to the minimum-norm solution of the SFP under appropriate conditions. In addition, we give some numerical examples to verify the implementation of our method. Our result improves and complements many known related results in the literature.