Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities

Volume 10, Issue 3, pp 1126--1147 http://dx.doi.org/10.22436/jnsa.010.03.23

Publication Date: March 20, 2017 Submission Date: December 19, 2016

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Authors

Lu-Chuan Ceng - Department of Mathematics, Shanghai Normal University; and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China. Yeong-Cheng Liou - Department of Healthcare Administration and Medical Informatics; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80702, Taiwan. Ching-Feng Wen - Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80702, Taiwan. - Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80702, Taiwan. Abdul Latif - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

In this paper, we introduce and analyze a hybrid steepest-descent viscosity algorithm for solving the triple hierarchical variational inequality problem with constraints of two problems: one generalized mixed equilibrium problem and another bilevel variational inequality problem in a real Hilbert space. Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is established. Our results improve and extend the corresponding results in the earlier and recent literature.

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Keywords

• Hybrid steepest-descent viscosity method
• triple hierarchical variational inequality
• generalized mixed equilibrium problem.

MSC

•  49J30
•  47H09
•  47J20
•  49M05

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