Exponential convergence of a proximal projection neural network for mixed variational inequalities and applications

Abstract

This paper proposes a novel proximal projection neural network (PPNN) to deal with mixed variational inequalities. It is shown that the PPNN has a unique continuous solution under the condition of Lipschitz continuity and that the trajectories of the PPNN converge to the unique equilibrium solution exponentially under some mild conditions. In addition, we study the influence of different parameters on the convergence rate. Furthermore, the proposed PPNN is applied in solving nonlinear complementarity problems, min–max problems, sparse recovery problems and classification and feature selection problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network.