STRONG CONVERGENCE THEOREM FOR SOLVING QUASI-MONOTONE VARIATIONAL INEQUALITY PROBLEMS.

In this paper, we propose a Mann type self-adaptive Tseng's extragradient method for solving the classical variational inequality problem with a Lipschitz continuous and quasi-monotone mapping in a real Hilbert space. The strong convergence of the proposed algorithm is proven without the prior knowledge of the Lipschitz constant of the corresponding function. Finally, we give some numerical examples to illustrate the superiority of our proposed algorithm. [ABSTRACT FROM AUTHOR]