Fast gradient descent algorithm for image classification with neural networks

Any optimization of gradient descent methods involves selecting a learning rate. Tuning the learning rate can quickly become repetitive with deeper models of image classification, does not necessarily lead to optimal convergence. We proposed in this paper, a modification of the gradient descent algorithm in which the Nestrove step is added, and the learning rate is update in each epoch. Instead, we learn learning rate itself, either by Armijo rule, or by control step. Our algorithm called fast gradient descent (FGD) for solving image classification with neural networks problems, the quadratic convergence rate o(k2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$o(k^2)$$\end{document} of FGD algorithm are proved. FGD algorithm are applicate to a MNIST dataset. The numerical experiment, show that our approach FGD algorithm is faster than gradient descent algorithms.