SOLVING CONVEX-PROGRAMMING PROBLEMS WITH EQUALITY CONSTRAINTS BY NEURAL NETWORKS

This paper presents a neural network approach for solving convex progr amming problems with equality constraints. After defining the energy f unction and neural dynamics of the proposed neural network, we show th e existence of an equilibrium point at which the neural dynamics becom es asymptotically stable. It is shown that under proper conditions, an optimal solution of the underlying convex programming problems is an equilibrium point of the neural dynamics, and vise verse. The configur ation of the proposed neural network with an exact layout is provided for solving linear programming problems. The operational characteristi cs of the neural network are demonstrated by numerical examples. (C) 1 998 Elsevier Science Ltd. All rights reserved.