# Convergence and Cycling in Walker-type Saddle Search Algorithms

arXiv: https://arxiv.org/abs/1607.08875 · HTML: https://mlsanity.com/paper/1607.08875/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2016.

## Built on by (most cited first, 2 of 2)

- [Staying the course: Locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds](https://mlsanity.com/paper/2204.10413/) (2022)
- [Gentlest ascent dynamics on manifolds defined by adaptively sampled point-clouds](https://mlsanity.com/paper/2302.04426/) (2023)

## Abstract (arXiv)

Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present results for idealized versions of the dimer and gentlest ascent (GAD) saddle search algorithms that show-case the limitations of what is theoretically achievable within the current class of saddle search algorithms: (1) we present an improved estimate on the region of attraction of saddles; and (2) we construct quasi-periodic solutions which indicate that it is impossible to obtain globally convergent variants of dimer and GAD type algorithms.