A Delayed Neural Network for Solving a Class of Constrained Pseudoconvex Optimizations

Abstract

This paper presents a delayed neural network (DNN) to solve a pseudoconvex optimization problem with equality constraints. Based on differential inclusion theory, the equilibrium point of the proposed DNN is proved to be exponentially stable. Moreover, for any initial value, the state of the DNN reaches equality constraint set in finite time and finally converges to an optimal solution to the pseudoconvex optimization problem. As far as we know, it is the first time that DNN is applied to solve pseudoconvex optimization problems. Compared with the existing neural networks for solving pseudoconvex optimization problems, the neural network here considers the time delays appearing in signal transmission. Furthermore, unlike convergence results based on complicated conditions, the convergence of states to the proposed DNN in this paper only rely on the assumption that the gradient of objective function in the pseudoconvex optimization problem is Lipschitz continuous. Finally, an examples is given to show the effectiveness of the proposed DNN.