New hybrid algorithm based on nonmonotone spectral gradient and simultaneous perturbation

Zineb Tabbakh (1) , Rachid Ellaia (1) , Abderrahmane Habbal (2, 3)

1 LERMA - Laboratoire d'Etudes et Recherche en Mathématiques Appliquées
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
3 LJAD - Laboratoire Jean Alexandre Dieudonné

In this paper, we introduce a new hybrid method called nonmonotone spectral gradient and simultaneous perturbation (NSGSP). It combines the advantages of nonmonotone spectral gradient (NSG), and simultaneous perturbation (SP) methods. The main idea of our approach is to use the simultaneous perturbation (SP) method in order to get a non expensive estimate of the gradient, and exploit the good properties of the nonmonotone spectral gradient (NSG) method in order to compute an efficient line search. Several numerical experiments are provided. The results indicate that the new method is effective and outperforms most of other popular methods.

Mots clés: Nonmonotone line search; Spectral gradient method; Simultaneous perturbation stochastic approximation

Domaines: Optimisation et contrôle [math.OC]

Zineb Tabbakh, Rachid Ellaia, Abderrahmane Habbal. New hybrid algorithm based on nonmonotone spectral gradient and simultaneous perturbation. International Journal of Mathematical Modelling and Numerical Optimisation, 2019, 9 (1), pp.1-23. ⟨10.1504/IJMMNO.2019.096911⟩. ⟨hal-01944548⟩