Convergence analysis of an inertial method for a system of general quasi-variational inequalities under mild conditions

Abstract

 In this paper, we propose an efficient inertial iterative algorithm for solving a system of generalized quasi-variational inequalities (SGQVI) in Hilbert spaces. Using the projection operator technique, we establish an equivalence between SGQVI and fixed-point problems, thus developing a novel inertial method. The algorithm introduces an inertial term to accelerate convergence, and its performance is rigorously analyzed under some mild conditions, including relaxed co-coercivity and Lipschitz continuity of the involved mappings. Our framework unifies and extends several existing models, such as classical variational inequalities, quasi-variational inequalities, and related optimization problems. Some experiments demonstrate the effectiveness of the inertial method, which shows an improvement in convergence speed compared to noninertial methods. Our results generalize and enhance previous research results in the literature, making it more widely applicable in computational mathematics, engineering, and economics.