Related papers: Identification of mechanisms of magnetic transitio…

A computational framework is presented for the sampling of the energy surface of magnetic systems via the systematic identification of first-order saddle points that determine connectivity of metastable states and define the mechanisms of…

Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of…

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…

Finding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle points. Without requiring Hessian information,…

We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any…

Various transitions that a magnetic skyrmion can undergo are found in calculations using a method for climbing up the energy surface and converging onto first order saddle points. In addition to collapse and escape through a boundary, the…

We present a scheme improving the minimum-mode following method for finding first order saddle points by confining the displacements of atoms to the subset of those subject to the largest force. By doing so it is ensured that the…

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…

Efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line…

Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been…

We introduce a new stochastic algorithm to locate the index-1 saddle points of a function $V:\mathbb R^d \to \mathbb R$, with $d$ possibly large. This algorithm can be seen as an equivalent of the stochastic gradient descent which is a…

Large-scale non-convex optimization problems are expensive to solve due to computational and memory costs. To reduce the costs, first-order (computationally efficient) and asynchronous-parallel (memory efficient) algorithms are necessary to…

The process of finding activated transitions in localized spin systems with continuous degrees of freedom is developed based on a magnetic variant of the Activation-Relaxation Technique (mART). In addition to the description of the method…

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…

Saddle points play important roles as the transition states of activated process in gradient system driven by energy functional. However, for the same energy functional, the saddle points, as well as other stationary points, are different…

First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…

Computing saddle points with a prescribed Morse index on potential energy surfaces is crucial for characterizing transition states for nosie-induced rare transition events in physics and chemistry. Many numerical algorithms for this type of…

An algorithm for the minimization of the energy of magnetic systems is presented and applied to the analysis of thermal configurations of a ferromagnet to identify inherent structures, i.e. the nearest local energy minima, as a function of…

A game theory inspired methodology is proposed for finding a function's saddle points. While explicit descent methods are known to have severe convergence issues, implicit methods are natural in an adversarial setting, as they take the…

We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…