An self-adaptive LQP method for constrained variational inequalities

In this paper, we present a logarithmic-quadratic proximal (LQP) type prediction-correction methods for solving constrained variational inequalities VI(S,f), where S is a convex set with linear constraints. The computational load in each iteration is quite tiny. However, the number of iterations is significantly dependent on a parameter which balances the primal and dual variables. We then propose a self-adaptive prediction-correction method that adjusts the scalar parameter automatically. Under certain conditions, the global convergence of the proposed method is established. In order to demonstrate the efficiency of the proposed method, we provide numerical results for a convex nonlinear programming and traffic equilibrium problems.