Fractional Order Euler-Lagrange Model for Accelerated Gradient Methods

In this study, a fractional order equation of motion as a continuous limit model for a family of gradient descent algorithms is discussed based on fractional order Euler-Lagrange equation. The aim of this proposed scheme is to search the ability to go beyond Nesterov scheme by introducing the potential of fractional calculus. The discretized version of the "designed" fractional order equation of motion (FO- EOM) forms new gradient descent algorithm that has been tested on some optimization benchmark functions to fairly assess the performance in comparison with the standard and accelerated form of gradient descent algorithms. Promising results have been obtained with more rigorous mathematical analysis has to be carried out as our future work. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)