Solving complementarity and variational inequalities problems using neural networks

In this paper, we propose a recurrent neural network model for solving a class of monotone variational inequalities problem with linear constraints. The neural network is stable in the sense of Lyapunov and globally convergent to an optimal solution. Compared with the existing convergence results, the present proof do not require Lipschitz continuity condition on the objective function. This neural network model has no adjustable parameter thus its structure is very simple. Variational inequalities problem with general set of constraints plus a general form of the complementarity problems are solved using the proposed neural networks. Some examples demonstrated to show the applicability of the proposed neural networks to solve various nonlinear optimization problems numerically.