Open AccessMultistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities
Author(s) -
Zhao-Rong Kong,
Lu-Chuan Ceng,
Qamrul Hasan Ansari,
Chin-Tzong Pang
Publication year - 2013
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2013/718624
Subject(s) - variational inequality , mathematics , intersection (aeronautics) , sequence (biology) , convergence (economics) , fixed point , set (abstract data type) , solution set , point (geometry) , mathematical optimization , mathematical analysis , computer science , geometry , biology , economic growth , engineering , economics , genetics , programming language , aerospace engineering
We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI
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