A parallel subgradient method extended to variational inequalities involving nonexpansive mappings. Issue 16 (9th December 2020)

• Record Type: Journal Article
• Authors: Anh, Pham Ngoc; Hien, Nguyen Duc; Phuong, Ngo Xuan
• Is Part Of: Applicable analysis. Volume 99:Issue 16(2020)
• Page Start: 2776
• Page End: 2792
• Publication Date: 2020-12-09
• Subjects: B. Mordukhovich; Fixed point -- pseudomonotonicity -- variational inequality -- subgradient projection method -- nonexpansive mapping; 65 K10 -- 90 C25 -- 49 J35 -- 47 J25 -- 91B50; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1584288
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we propose and analyze the convergence of new iteration methods for finding a common point of the solution set of a class of pseudomonotone variational inequalities and the fixed point set of a finite system of nonexpansive mappings in a real Hilbert space. The idea of this algorithm is to combine the subgradient method with the parallel splitting-up techniques. The main iteration step in the proposed methods uses only one projection and does not require any Lipschitz continuous condition for the cost mapping. The convergent results are also extended to a pseudomonotone equilibrium problem involving a finite system of nonexpansive mappings. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.