An Inertial Projection Neural Network for Solving Variational Inequalities
提出一种带惯性项的投影神经网络，用于求解单调变分不等式及相关约束优化问题，相比现有方法能克服最速下降法的缺陷，并适用于非凸优化问题的KKT最优解探索。
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.