Constrained high-index saddle dynamics for the solution landscape with equality constraints
Numerical Analysis
2025-11-20 v4 Numerical Analysis
Abstract
We propose a constrained high-index saddle dynamics (CHiSD) method to search for index- saddle points of an energy functional subject to equality constraints. With Riemannian manifold tools, the CHiSD is derived in a minimax framework, and its linear stability at an index- saddle point is proved. To ensure the manifold property, the CHiSD is numerically implemented using retractions and vector transport. Then we present a numerical approach by combining CHiSD with downward and upward search algorithms to construct the solution landscape in the presence of equality constraints. We apply the Thomson problem and the Bose-Einstein condensation as numerical examples to demonstrate the efficiency of the proposed method.
Keywords
Cite
@article{arxiv.2011.13173,
title = {Constrained high-index saddle dynamics for the solution landscape with equality constraints},
author = {Jianyuan Yin and Zhen Huang and Lei Zhang},
journal= {arXiv preprint arXiv:2011.13173},
year = {2025}
}