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.

摘要

大量的非线性和优化问题可以简化为变点问题。本文旨在介绍并行正态 S 迭代技术并研究其在实际假设下解决无限维希尔伯特空间中此类问题的收敛速度。我们特别强调了两个最大单调算子之和的并行分裂方法，它可以应用于解决一类凸复合最小化问题。此外，我们将迭代方法应用于一些非线性问题，例如变分不等式系统和包含问题系统。最后，为了证明变点技术的适用性，