Parallel proximal method of solving split system of fixed point set constraint minimization problems

Abstract

The purpose of this paper is to introduce iterative algorithm solving split system of fixed point set constraint minimization problem given as a task of finding a fixed point $$\bar{x}$$ of a strictly pseudocontractive mapping and is also a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image $$A(\bar{x})$$ under a bounded linear operator A is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. Our algorithm is designed by introducing a setting that will allow us avoid the necessity of prior knowledge of the operator norm to determine the step sizes. Some applications and numerical experiment is given to analyse the efficiency of our algorithm.