A unified extragradient method for systems of hierarchical variational inequalities in a Hilbert space

Journal of inequalities and applications

Lu-Chuan Ceng¹ 

关键词: system of hierarchical variational inequalities;    generalized mixed equilibrium problem;    variational inclusion;    variational inequality problem;    multistep Mann-type extragradient method;    fixed point;   

DOI  :  10.1186/1029-242X-2014-460

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY