A STRONGLY CONVERGENT SELF-ADAPTIVE INERTIAL ALGORITHM FOR BILEVEL EQUILIBRIUM PROBLEMS IN HILBERT SPACES

Abstract

In this work, we introduce a novel modified inertial iterative algorithm for solving bilevel equilibrium problems involving pseudomonotone bifunctions in real Hilbert spaces. Theproposed scheme incorporates a self-adaptive step-size strategy, eliminating the need for prior knowledge of Lipschitz type constants and enhancing its practical applicability. Under mild and easily verifiable assumptions, we establish the strong convergence of the algorithm to the unique solution of the bilevel equilibrium problem. The convergence analysis relies on a set of innovative techniques that differ significantly from existing approaches in the literature, thereby contributing new theoretical insights to the study of equilibrium problems. In addition, we provide comprehensive numerical experiments to demonstrate the effectiveness and robustness of the proposed method. Comparative results indicate that our algorithm outperforms several well-known iterative schemes in terms of convergence speed and computational efficiency, making it a promising tool for solving complex hierarchical equilibrium models.