Solving convex programming problems with equality constraints by neural networks

This paper presents a neural network approach for solving convex programming problems with equality constraints. After defining the energy function and neural dynamics of the proposed neural network, we show the existence of an equilibrium point at which the neural dynamics becomes 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 versa. The configuration of the proposed neural network with an exact layout is provided for solving linear programming problems. The operational characteristics of the neural network are demonstrated by numerical examples.