Efficient extragradient methods for bilevel pseudomonotone variational inequalities with non-Lipschitz operators and their applications



	Efficient extragradient methods for bilevel pseudomonotone variational inequalities with non-Lipschitz operators and their applications


	Fixed Point Theory, Volume 25, No. 1, 2024, 309-332, February 1st, 2024 DOI: 10.24193/fpt-ro.2024.1.19 Authors: X. Qin, A. Petrușel, B. Tan and J.C. Yao Abstract: In this paper, four extragradient-type algorithms are presented for solving bilevel variational inequalities of pseudomonotone and non-Lipschitz continuous operators in real Hilbert spaces. The proposed iterative schemes employ two Armijo-type linesearch methods making them work adaptively. Strong convergence theorems of the suggested algorithms are established under some mild conditions. Finally, some numerical experiments and applications are given to verify the advantages and efficiency of the proposed algorithms over some previously known ones. Key Words and Phrases: Bilevel variational inequality problem, inertial extragradient method, Armjio stepsize, pseudomonotone mapping, non-Lipschitz operator, fixed point. 2010 Mathematics Subject Classification: 65K15, 90C30, 47H10. Published on-line: February 1st, 2024. Fulltext pdf Back to volume's table of contents