Convergence Analysis of Tseng's Extragradient Method for Variational Inequalities with uniformly continuous Operators

In this paper, we consider variational inequality problems in real Hilbert spaces characterized by uniformly continuous and quasimonotone operators. To address them, we adopt Tseng's extragradient method equipped with a self-adaptive stepsize. Convergence of the proposed approach is established under mild assumptions. The key advantage of this method lies in its ability to eliminate the need for the Lipschitz continuity assumption while employing a self-adaptive step size strategy that avoids any line search procedure. In addition, our theoretical analysis establishes an original framework for solving variational inequalities with non-Lipschitz operators. Numerical experiments are further conducted to highlight the method's efficiency and advantages. Mathematics Subject Classification (2010). 47H05; 47J20; 47J25; 90C25.