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

作者：Ceng, Lu-Chuan; Liou, Yeong-Cheng; Wen, Ching-Feng^*

来源：Journal of Nonlinear Sciences and Applications, 2016, 9(6): 4052-4069.

DOI：10.22436/jnsa.009.06.49

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

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.

• 出版日期2016
• 单位上海师范大学