Parallel Normal S-Iteration Methods with Applications to Optimization Problems. (30th March 2022)

• Record Type: Journal Article
• Authors: Xu, Hong-Kun; Sahu, D. R.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 16(2021)
• Page Start: 1925
• Page End: 1953
• Publication Date: 2022-03-30
• Subjects: Convex optimization -- maximal monotone operator -- nonexpansive mapping -- proximal gradient method -- resolvent -- S-iteration method -- variational inequality; 47J05 -- 47H09 -- 65K05 -- 65K10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1950761
• Languages: English
• ISSNs: 0163-0563

Abstract

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.