Smoothing Neural Network for Non-Lipschitz Optimization with Linear Inequality Constraints

This paper presents a smoothing neural network to solve a class of non-Lipschitz optimization problem with linear inequality constraints. The proposed neural network is modelled with a differential inclusion equation, which introduces the smoothing approximate techniques. Under certain conditions, we prove that the trajectory of neural network reaches the feasible region in finite time and stays there thereafter, and that any accumulation point of the solution is a stationary point of the original optimization problem. Furthermore, if all stationary points of the optimization problem are isolated, then the trajectory converges to a stationary point of the optimization problem. Two typical numerical examples are given to verify the effectiveness of the proposed neural network.