# The Gradient descent method from the perspective of fractional calculus

arXiv: https://arxiv.org/abs/1911.08058 · HTML: https://mlsanity.com/paper/1911.08058/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2019.

## Built on by (most cited first, 3 of 3)

- [A Caputo fractional derivative-based algorithm for optimization](https://mlsanity.com/paper/2104.02259/) (2021)
- [Convergence Analysis of Fractional Gradient Descent](https://mlsanity.com/paper/2311.18426/) (2023)
- [Applications of fractional calculus in learned optimization](https://mlsanity.com/paper/2411.14855/) (2024)

## Abstract (arXiv)

Motivated by gradient methods in optimization theory, we give methods based on psi-fractional derivatives of order α in order to solve unconstrained optimization problems. The convergence of these methods is analyzed in detail. This paper also presents an Adams-Bashforth-Moulton (ABM) method for the estimation of solutions to equations involving psi-fractional derivatives. Numerical examples using the ABM method show that the fractional order α and weight psi are tunable parameters, which can be helpful for improving the performance of gradient descent methods.