DOI: 10.24193/fpt-ro.2024.1.14

Authors: Yinglin Luo, Jingjing Fan and Songxiao Li

Abstract: In this paper, a self-adaptive algorithm involving inertial technique will be introduced to solve bilevel pseudo-monotone variational inequality problems in Hilbert spaces. The main advantages of our algorithm is that the strong convergence theorem of the stated iterative method is proved without Lipschitz continuity condition of the associated mapping. Finally, the effectiveness and superiority of the proposed algorithm are proposed by numerical experiments.

Key Words and Phrases: Inertial algorithm, pseudo-monotone mapping, bilevel variational inequality problem, strong convergence, fixed point, Hilbert space.

2010 Mathematics Subject Classification: 49J40, 47H06, 47H10, 90C30, 47N10, 47H09.

Published on-line: February 1st, 2024.

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