A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions
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Authors
Lu-Chuan Ceng
- Department of Mathematics, Shanghai Normal University, Shanghai 200234, China.
Yeong-Cheng Liou
- Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan.
- Research Center of Nonlinear Analysis and Optimization and Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan.
Ching-Feng Wen
- Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan.
Abstract
In this paper, we introduce and analyze a hybrid extragradient algorithm for solving bilevel pseudomonotone
variational inequalities with multiple solutions in a real Hilbert space. The proposed algorithm is based
on Korpelevich's extragradient method, Mann's iteration method, hybrid steepest-descent method, and viscosity
approximation method (including Halpern's iteration method). Under mild conditions, the strong
convergence of the iteration sequences generated by the algorithm is derived.
Share and Cite
ISRP Style
Lu-Chuan Ceng, Yeong-Cheng Liou, Ching-Feng Wen, A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4052--4069
AMA Style
Ceng Lu-Chuan, Liou Yeong-Cheng, Wen Ching-Feng, A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions. J. Nonlinear Sci. Appl. (2016); 9(6):4052--4069
Chicago/Turabian Style
Ceng, Lu-Chuan, Liou, Yeong-Cheng, Wen, Ching-Feng. "A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4052--4069
Keywords
- Bilevel variational inequality
- hybrid extragradient algorithm
- pseudomonotonicity
- Lipschitz continuity
- global convergence.
MSC
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