On a Stabilization Problem of Nonlinear Programming Neural Networks

Abstract

Intrinsically, Lagrange multipliers in nonlinear programming algorithms play a regulating role in the process of searching optimal solution of constrained optimization problems. Hence, they can be regarded as the counterpart of control input variables in control systems. From this perspective, it is demonstrated that constructing nonlinear programming neural networks may be formulated into solving servomechanism problems with unknown equilibrium point which coincides with optimal solution. In this paper, under second-order sufficient assumption of nonlinear programming problems, a dynamic output feedback control law analogous to that of nonlinear servomechanism problems is proposed to stabilize the corresponding nonlinear programming neural networks. Moreover, the asymptotical stability is shown by Lyapunov First Approximation Principle.