Relaxed Two-Step Inertial Tseng’s Extragradient Method for Nonmonotone Variational Inequalities - Viet Thong, Duong; Ky Anh, Pham; Tien Dung, Vu (Journal of optimization theory and applications, 2025)
This work introduces a novel inertial projection method for solving the variational inequality (VI) without imposing the restrictive assumption of monotonicity on the cost operator. We establish global convergence of the proposed method under the condition that the solution set of the associated Minty VI with it is non-empty. Our results improve upon and extend many important related results in this research direction, providing a more general and flexible framework for tackling non-monotone variational inequalities. To demonstrate the practical efficacy of our method, we give some numerical illustrations and apply the proposed algorithm to solve a network equilibrium flow problem, which is a fundamental problem in transportation infrastructure modeling. We also compare the performance of our algorithm with those of existing ones.