An Iterative Minimization Formulation for Saddle-Point Search

TL;DR

This paper introduces an iterative minimization approach for efficiently locating index-1 saddle points in energy functions, achieving quadratic convergence and extending to higher index saddle points and constrained manifolds.

Contribution

It presents a novel iterative minimization formulation that outperforms existing methods by providing quadratic convergence for saddle point search.

Findings

Achieves quadratic convergence rate for saddle point search

Generalizes methodology to higher index saddle points

Extends approach to constrained energy functions on manifolds

Abstract

This paper proposes and analyzes an iterative minimization formulation for search- ing index-1 saddle points of an energy function. This formulation differs from other eigenvector-following methods by constructing a new objective function near the guess at each iteration step. This leads to a quadratic convergence rate, in comparison to the linear case of the gentlest ascent dynamics (E and Zhou, nonlinearity, vol 24, p1831, 2011) and many other existing methods. We also propose the generalization of the new methodology for saddle points of higher index and for constrained energy functions on manifold.