Dynamical Systems and Nonconvex Quadratic Programs

Abstract

This paper studies a dynamical system approach for solving indefinite quadratic programming problems subject to linear constraints. We investigate the convergence of the trajectory generated by the system to a Karush-Kuhn-Tucker point of the quadratic programs. In addition, we derive an estimate for the distance between the trajectory and a solution of the problem. We further prove that the objective value is decreasing along the trajectory. An illustrative example and a numerical test are presented to demonstrate the behavior and performance of the proposed method.