A Recurrent Neural Network for Non-smooth Nonlinear Programming Problems

Abstract

A recurrent neural network is proposed for solving non-smooth nonlinear programming problems, which can be regarded as a generalization of the smooth nonlinear programming neural network used in (X.B. Gao, 2004). Based on the non-smooth analysis and the theory of differential inclusions, the proposed neural network is demonstrated to be globally convergent to the exact optimal solution of the original optimization problem. Compared with the existing neural networks, the proposed approach takes both equality and inequality constraints into account, and no penalty parameters have to be estimated beforehand. Therefore, it can solve a larger class of non-smooth programming problems. Finally, several illustrative examples are given to show the effectiveness of the proposed neural network.