A Hybrid Direction Algorithm for Solving a Convex Quadratic Problem

Abstract

In this paper, we propose a new algorithm for solving convex quadratic programming problems with bounded variables. Instead of using the standard direction of the adaptive method, which is constructed by minimising only the linear part of the objective function increment, we will suggest a new descent direction, called 'hybrid direction'. This latter is constructed by minimising a quadratic part of the increment. Furthermore, we define a quantity called 'optimality estimate' from which we derive sufficient and necessary conditions of optimality. On the basis of this new concept, we construct an algorithm for solving convex quadratic programs. In order to compare our method with the active-set method implemented in MATLAB, numerical experiments on randomly generated test problems are presented.