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Open AccessArticle

On a General Extragradient Implicit Method and Its Applications to Optimization

by Lu-Chuan Ceng 1 and Qing Yuan 2,*
1
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2
School of Mathematics and Statistics, Linyi University, Linyi 276000, China
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 124; https://doi.org/10.3390/sym12010124
Received: 19 November 2019 / Revised: 2 January 2020 / Accepted: 6 January 2020 / Published: 8 January 2020
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
Let X be a Banach space with both q-uniformly smooth and uniformly convex structures. This article introduces and considers a general extragradient implicit method for solving a general system of variational inequalities (GSVI) with the constraints of a common fixed point problem (CFPP) of a countable family of nonlinear mappings { S n } n = 0 and a monotone variational inclusion, zero-point, problem. Here, the constraints are symmetrical and the general extragradient implicit method is based on Korpelevich’s extragradient method, implicit viscosity approximation method, Mann’s iteration method, and the W-mappings constructed by { S n } n = 0 . View Full-Text
Keywords: variational inclusions; general extragradient implicit method; variational systems; norm convergence. variational inclusions; general extragradient implicit method; variational systems; norm convergence.
MDPI and ACS Style

Ceng, L.-C.; Yuan, Q. On a General Extragradient Implicit Method and Its Applications to Optimization. Symmetry 2020, 12, 124.

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