Improving the Robustness of Difference of Convex Algorithm in the Research of a Global Optimum of a Nonconvex Differentiable Function Defined on a Bounded Closed Interval

Leslous Fadila (1) , Philippe Marthon (2, 3) , Ouanes Mohand (1)

1 Laboratoire de Recherche Opérationnelle et Mathématiques de la Décision - LAROMAD (Alger, Algérie)
2 IRIT-TCI - Traitement et Compréhension d’Images
3 Toulouse INP - Institut National Polytechnique (Toulouse)

In this paper we present an algorithm for solving a DC problem non convex on an interval [a, b] of R. We use the DCA (Difference of Convex Algorithm) and the minimum of the average of two approximations of the function from a and b.This strategy has the advantage of giving in general a minimum to be situated in the attraction zone of the global minimum searched. After applying the DCA from this minimum we certainly arrive at the global minimum searched.

Mots clés: Optimization DC And DCA; Non Convex Optimization; Global Optimization

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Leslous Fadila, Philippe Marthon, Ouanes Mohand. Improving the Robustness of Difference of Convex Algorithm in the Research of a Global Optimum of a Nonconvex Differentiable Function Defined on a Bounded Closed Interval. Applied Mathematical Sciences, 2014, vol. 8 (n° 1), pp. 1-12. ⟨10.12988/ams.2014.35258⟩. ⟨hal-01137376v2⟩