Related papers: A spring pair method of finding saddle points usin…

Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the…

Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. In recent years, several variance-reduced PG methods have been proposed with a theoretical guarantee of converging to an approximate…

In this paper, based a novel primal-dual dynamical model with adaptive scaling parameters and Bregman divergences, we propose new accelerated primal-dual proximal gradient splitting methods for solving bilinear saddle-point problems with…

Saddle-point systems appear in many scientific and engineering applications. The systems can be sparse, symmetric or nonsymmetric, and possibly singular. In many of these applications, the number of constraints is relatively small compared…

We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize…

Primal-dual algorithms for the resolution of convex-concave saddle point problems usually come with one or several step size parameters. Within the range where convergence is guaranteed, choosing well the step size can make the difference…

We develop an efficient numerical algorithm for the identification of a large number of saddle points of the potential energy function of Lennard- Jones clusters. Knowledge of the saddle points allows us to find many thousand adjacent…

Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models efficiently. First-order methods such as gradient descent are usually the methods of choice for training machine…

Safety and automatic control are extremely important when operating manipulators. For large engineering manipulators, the main challenge is to accurately recognize the posture of all arm segments. In classical sensing methods, the accuracy…

We report a detailed study of the stationary points (zero-force points) of the potential energy surface (PES) of a model structural glassformer. We compare stationary points found with two different algorithms (eigenvector following and…

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where…

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…

The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection…

We propose the nullspace-preserving high-index saddle dynamics (NPHiSD) method for degenerating multiple solution systems in constrained and unconstrained settings. The NPHiSD efficiently locates high-index saddle points and provides parent…

We introduce a robust numerical method for determining intersection numbers of Lefschetz thimbles in multivariable settings. Our approach employs the multiple shooting method to solve the upward flow equations from the saddle points to the…

In this work, we consider the optimization formulation for symmetric tensor decomposition recently introduced in the Subspace Power Method (SPM) of Kileel and Pereira. Unlike popular alternative functionals for tensor decomposition, the SPM…

The Minima Hopping global optimization method uses physically realizable molecular dynamics moves in combination with an energy feedback that guarantees the escape from any potential energy funnel. For the purpose of finding reactions…

We describe a method to track particles undergoing large displacements. Starting with a list of particle positions sampled at different time points, we assign particle identities by minimizing the sum across all particles of the trace of…

We present a unified framework based on primal-dual stochastic mirror descent for approximately solving infinite-horizon Markov decision processes (MDPs) given a generative model. When applied to an average-reward MDP with $A_{tot}$ total…

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…