A Novel Collaborate Neural Dynamic System Model for Solving a Class of Min–Max Optimization Problems with an Application in Portfolio Management

Abstract

In this paper, we describe a new neural network model for solving a class of non-smooth optimization problems with min–max objective function. The basic idea is to replace the min–max function by a smooth one using an entropy function. With this smoothing technique, the non-smooth problem is converted into an equivalent differentiable convex programming problem. A neural network model is then constructed based on Karush–Kuhn–Tucker optimality conditions. It is investigated that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. As an application in economics, we use the proposed scheme to a min–max portfolio optimization problems. The effectiveness of the method is demonstrated by several numerical simulations.