A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions

Volume 9, Issue 6, pp 4052--4069 http://dx.doi.org/10.22436/jnsa.009.06.49

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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.

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Keywords

• Bilevel variational inequality
• hybrid extragradient algorithm
• pseudomonotonicity
• Lipschitz continuity
• global convergence.

MSC

•  49J30
•  47H09
•  47J20
•  49M05

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