Parallel Normal S-Iteration Methods with Applications to Optimization Problems

Abstract

A large number of nonlinear and optimization problems can be reduced to altering point problems. This paper aims to introduce the parallel normal S-iteration technique and study its convergence rates for solving such problems in infinite-dimensional Hilbert spaces under practical assumptions. We place particular emphasis on the parallel splitting method for the sum of two maximal monotone operators and that can apply for solving a class of convex composite minimization problems. Moreover, we present applications of our iterative methods to some nonlinear problems, such as a system of variational inequalities and a system of inclusion problems. Finally, to demonstrate the applicability of the altering point technique, the performances of our proposed parallel normal S-iteration methods are presented through numerical experiments in signal recovery problems.