A unified extragradient method for systems of hierarchical variational inequalities in a Hilbert spaceReport as inadecuate




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Journal of Inequalities and Applications

, 2014:460

Thematic series on Nonlinear Analysis and Optimization

Abstract

In this paper, we introduce and analyze a multistep Mann-type extragradient iterative algorithm by combining Korpelevich’s extragradient method, viscosity approximation method, hybrid steepest-descent method, Mann’s iteration method, and the projection method. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings and a strict pseudocontraction, the solution set of finitely many generalized mixed equilibrium problems GMEPs, the solution set of finitely many variational inclusions and the solution set of a variational inequality problem VIP, which is just a unique solution of a system of hierarchical variational inequalities SHVI in a real Hilbert space. The results obtained in this paper improve and extend the corresponding results announced by many others.

MSC: 49J30, 47H09, 47J20, 49M05.

Keywordssystem of hierarchical variational inequalities generalized mixed equilibrium problem variational inclusion variational inequality problem multistep Mann-type extragradient method fixed point  Download fulltext PDF



Author: Lu-Chuan Ceng - Daya Ram Sahu - Jen-Chih Yao

Source: https://link.springer.com/







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