An Inertial Projection Neural Network for Solving Variational Inequalities

Recently, projection neural network (PNN) was proposed for solving monotone variational inequalities (VIs) and related convex optimization problems. In this paper, considering the inertial term into first order PNNs, an inertial PNN (IPNN) is also proposed for solving VIs. Under certain conditions, the IPNN is proved to be stable, and can be applied to solve a broader class of constrained optimization problems related to VIs. Compared with existing neural networks (NNs), the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different Karush-Kuhn-Tucker optimal solution for nonconvex optimization problems. Finally, simulation results on three numerical examples show the effectiveness and performance of the proposed NN.