Title: A hybrid direction algorithm for solving a convex quadratic problem

Authors: Mohand Ouamer Bibi; Nacira Ikheneche; Mohand Bentobache

Addresses: Research Unit LaMOS (Modeling and Optimization of Systems), University of Bejaia, Bejaia, 06000, Algeria ' Research Unit LaMOS (Modeling and Optimization of Systems), University of Bejaia, Bejaia, 06000, Algeria ' Laboratory of Pure and Applied Mathematics, University of Laghouat, Laghouat, 03000, Algeria

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.

Keywords: convex quadratic programming; adaptive method; bounded variables; hybrid direction; optimality estimate; numerical experiments.

DOI: 10.1504/IJMOR.2020.105862

International Journal of Mathematics in Operational Research, 2020 Vol.16 No.2, pp.159 - 178

Received: 30 Apr 2018
Accepted: 14 Oct 2018
Published online: 16 Mar 2020 *

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