Solving Mixed Variational Inequalities Via a Proximal Neurodynamic Network with Applications

摘要

This paper proposes a proximal neurodynamic network (PNDN) for solving mixed variational inequalities based on the proximal operator. It is shown that the proposed PNDN is globally exponentially stable under some mild conditions, and a stopping condition is provided for the PNDN. Furthermore, the proposed PNDN is applied in solving variational inequalities and composition optimization with nonsmooth regularization. In addition, the equilibrium point of the proposed proximal gradient neurodynamic network for composition optimization problems is globally exponentially stable via the Polyak-Lojasiewicz condition, a relaxation of strong convexity. Finally, numerical and experimental examples on sparse signal reconstruction and variational arc-flow problems are presented to validate the effectiveness of the proposed neurodynamic network.