A Logarithmic–Quadratic Proximal method for pseudomonotone variational inequalities

In this paper, we propose a modified Logarithmic–Quadratic Proximal (LQP) method for solving variational inequalities problems. We solved the problem approximately, with constructive accuracy criterion. We show that the method is globally convergent under that the operator is pseudomonotone which is weaker that the monotonicity and the solution set is nonempty. Some preliminary computational results are given.