An Approximation Technique for General Split Feasibility Problems Based on Projection onto the Intersection of Half-spaces

Abstract

This paper presents a novel relaxed CQ algorithm for solving the multiple-sets split feasibility problem with multiple output sets (MSSFPMOS) in infinite-dimensional real Hilbert spaces. The proposed method replaces the projection to half-space with the projection to the intersection of two half-spaces, resulting in accelerated convergence by utilizing previous half-spaces. The present study introduces a novel algorithm that dynamically determines the stepsize, without any a priori knowledge of the operator norm required. Furthermore, the algorithm is proven to exhibit strong convergence to the minimum-norm solution of the MSSFPMOS. Finally, a number of numerical experiments have been conducted to showcase the impressive performance of the proposed algorithm.