An Algorithm for Solving Quadratic Programming Problems with an M-matrix

Abstract

In this study, we propose an approach for solving a quadraticprogramming problem with an M-matrix and simple constraints (QPs). It isbased on the algorithms of Luk-Pagano and Stachurski. These methods usethe fact that an M-matrix possesses a nonnegative inverse which allows tohave a sequence of feasible points monotonically increasing. Introducing theconcept of support for an objective function developed by Gabasov et al., ourapproach leads to a more general condition which allows to have an initialfeasible solution, related to a coordinator support and close to the optimalsolution. The programming under MATLAB of our method and that of Lukand Pagano has allowed us to make a comparison between them, with anillustration on two numerical examples.