Title: New hybrid algorithm based on nonmonotone spectral gradient and simultaneous perturbation

Authors: Tabbakh Zineb; Ellaia Rachid; Habbal Abderrahmane

Addresses: LERMA Laboratory, Engineering for Smart and Sustainable Systems Research Center (E3S), Mohammadia School of Engineers, Mohammed V University of Rabat, Ibn Sina Avenue, CP 10050 Agdal, BP 765, Rabat, Morocco ' LERMA Laboratory, Engineering for Smart and Sustainable Systems Research Center (E3S), Mohammadia School of Engineers, Mohammed V University of Rabat, Ibn Sina Avenue, CP 10050 Agdal, BP 765, Rabat, Morocco ' Université Côte d'Azur, Inria, CNRS, LJAD, UMR 7351, Parc Valrose, 06108 Nice, France

Abstract: 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.

Keywords: nonmonotone line search; spectral gradient method; simultaneous perturbation stochastic approximation.

DOI: 10.1504/IJMMNO.2019.096911

International Journal of Mathematical Modelling and Numerical Optimisation, 2019 Vol.9 No.1, pp.32 - 55

Received: 19 Apr 2017
Accepted: 11 Dec 2017
Published online: 13 Dec 2018 *

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