A dynamic system approach for solving nonlinear programming problems with exact penalty function

Abstract

The Dynamic system has attracted increasing attention in recent years. In this paper, a dynamic system approach for solving Nonlinear Programming (NLP) problems with inequality constrained is presented. First, the system of differential equations based on exact penalty function is constructed. Furthermore, it is found that the equilibrium point of the dynamic system is converge to an optimal solution of the original optimization problem and is asymptotically stable in the sense of Lyapunov. Moreover, the Euler scheme is used for solving differential equations system. Finally, two practical examples are illustrated the effectiveness of the proposed dynamic system formulation.