A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate
Numerical Analysis
2026-01-07 v1 Numerical Analysis
Optimization and Control
Abstract
We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point search. Through rigorous numerical analysis, we prove the almost sure convergence of the inner step under suitable assumptions. Furthermore, we establish the convergence of the outer search using a decaying step size, while demonstrating linear convergence under constant step size and boundedness conditions. Numerical experiments are provided to validate our theoretical results and demonstrate the algorithm's practical applicability.
Cite
@article{arxiv.2601.02650,
title = {A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate},
author = {Qiang Du and Baoming Shi and Lei Zhang and Xiangcheng Zheng},
journal= {arXiv preprint arXiv:2601.02650},
year = {2026}
}