Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities
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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.
Share and Cite
ISRP Style
Lu-Chuan Ceng, Yeong-Cheng Liou, Ching-Feng Wen, Abdul Latif, Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1126--1147
AMA Style
Ceng Lu-Chuan, Liou Yeong-Cheng, Wen Ching-Feng, Latif Abdul, Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities. J. Nonlinear Sci. Appl. (2017); 10(3):1126--1147
Chicago/Turabian Style
Ceng, Lu-Chuan, Liou, Yeong-Cheng, Wen, Ching-Feng, Latif, Abdul. "Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1126--1147
Keywords
- Hybrid steepest-descent viscosity method
- triple hierarchical variational inequality
- generalized mixed equilibrium problem.
MSC
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