# Lipschitz gradients for global optimization in a one-point-based partitioning scheme

arXiv: https://arxiv.org/abs/1307.4302 · HTML: https://mlsanity.com/paper/1307.4302/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2013.

## Built on by (most cited first, 1 of 1)

- [An Efficient Global Optimization Algorithm with Adaptive Estimates of the Local Lipschitz Constants](https://mlsanity.com/paper/2211.04129/) (2022)

## Abstract (arXiv)

A global optimization problem is studied where the objective function f(x) is a multidimensional black-box function and its gradient f'(x) satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant K. Different methods for solving this problem by using an a priori given estimate of K, its adaptive estimates, and adaptive estimates of local Lipschitz constants are known in the literature. Recently, the authors have proposed a one-dimensional algorithm working with multiple estimates of the Lipschitz constant for f'(x) (the existence of such an algorithm was a challenge for 15 years). In this paper, a new multidimensional geometric method evolving the ideas of this one-dimensional scheme and using an efficient one-point-based partitioning strategy is proposed. Numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular DIRECT-based methods.