New hybrid algorithm based on nonmonotone spectral gradient and simultaneous perturbation

: 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. Habbal concern analysis and control of systems governed by partial differential equations (PDEs), optimization theory and algorithms and PDE-constrained games. Application fields are related to (nonlinear) mechanics, image processing, data recovering and cell dynamics.