# Super Gradient Descent: Global Optimization requires Global Gradient

arXiv: https://arxiv.org/abs/2410.19706 · HTML: https://mlsanity.com/paper/2410.19706/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 9 references that are in the map.
- First posted on arXiv 25 Oct 2024.

## Builds on (most cited first, 1 of 1)

- [A finite difference method with symmetry properties for the high-dimensional Bratu equation](https://mlsanity.com/paper/2410.12553/) (2024)

## Abstract (arXiv)

Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization method that we called Super Gradient Descent, designed specifically for one-dimensional functions, guaranteeing convergence to the global minimum for any k-Lipschitz function defined on a closed interval [a, b]. Our approach addresses the limitations of traditional optimization algorithms, which often get trapped in local minima. In particular, we introduce the concept of global gradient which offers a robust solution for precise and well-guided global optimization. By focusing on the global minimization problem, this work bridges a critical gap in optimization theory, offering new insights and practical advancements in different optimization problems in particular Machine Learning problems like line search.