Title: Algorithm and separating method for the optimisation of quadratic functions

Authors: Amel Belabbaci; Bachir Djebbar

Addresses: Laboratory of Computer Sciences and Mathematics, University of Laghouat, Laghouat, Algeria ' Department of Computer Sciences, Faculty of Mathematics and Computer Sciences, University of Sciences and Technology Mohamed Boudiaf, Oran, Algeria

Abstract: This paper addresses the optimisation of quadratic functions on convex polyhedrons. We propose a method and an algorithm for optimising a strictly concave function. This algorithm uses a good initialisation by searching the nearest vertex of a convex set to an external point in order to surround the area where the optimal solution can be located. The optimal solution may be the nearest vertex found or a boundary point obtained by the projection of the critical point onto a separating hyperplane passing through the nearest vertex. This method and this algorithm can be adapted for the convex quadratic problem. In this case, the optimal solution is the farthest vertex from the critical point.

Keywords: separating method; concave; quadratic function; optimisation; vertex; critical point; boundary point; maximising; separating hyperplane; convex.

DOI: 10.1504/IJCSM.2017.10004499

International Journal of Computing Science and Mathematics, 2017 Vol.8 No.2, pp.183 - 192

Accepted: 27 Sep 2016
Published online: 21 Apr 2017 *

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