The Tseng's Extragradient Method for Semistrictly Quasimonotone Variational Inequalities

Abstract

In this paper, we investigate the weak convergence of an iterative method for solving classical variational inequalities problems with semistrictly quasimonotone and Lipschitz-continuous mappings in real Hilbert space. The proposed method is based on Tseng's extragradient method and uses a set stepsize rule that is dependent on the Lipschitz constant as well as a simple self-adaptive stepsize rule that is independent of the Lipschitz constant. We proved a weak convergence theorem for our method without requiring any additional projections or the knowledge of the Lipschitz constant of the involved mapping. Finally, we offer some numerical experiments that demonstrate the efficiency and benefits of the proposed method. © 2022 Journal of Applied and Numerical Optimization.