A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions
Lu-Chuan Ceng, Yeong‐Cheng Liou, Ching‐Feng Wen · The Journal of Nonlinear Sciences and Applications · 2016
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.