Related papers: Towards sharp error analysis of extended Lagrangia…

Extended Lagrangian molecular dynamics (XLMD) is a general method for performing molecular dynamics simulations using quantum and classical many-body potentials. Recently several new XLMD schemes have been proposed and tested on several…

We present a new stochastic extended Lagrangian solution to charge equilibration that eliminates self-consistent field (SCF) calculations, eliminating the computational bottleneck in solving the many-body solution with standard SCF solvers.…

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) [Phys. Rev. Lett. vol. 100, 123004 (2008)] is combined with Kohn-Sham density functional theory (DFT) using a DFT+U correction based on the Hubbard model. This combined…

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…

Conventional molecular dynamics (MD) simulation approaches, such as $\textit{ab initio}$ MD (AIMD) and empirical force field MD (EFFMD), face significant trade-offs between physical accuracy and computational efficiency. This work presents…

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…

We introduce Variational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes and associated connectivity structures from multivariate signals. VLMD addresses key limitations of existing Multivariate Mode…

A fundamental objective of materials modeling is identifying atomic structures that align with experimental observables. Conventional approaches for disordered materials involve sampling from thermodynamic ensembles and hoping for an…

We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic orbital-free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a…

Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…

The recent progress of linear-scaling or O(N) methods in the density functional theory (DFT) is remarkable. We expect that first-principles molecular dynamics (FPMD) simulations based on DFT can now treat more realistic and complex systems…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

Aligning theoretical atomistic structural models of materials with available experimental data presents a significant challenge for disordered systems. The configurational space to navigate is vast, and faithful realizations require large…

Within the framework of the augmented Lagrangian (AL), we propose a novel distributed optimization method, termed Distributed Augmented Lagrangian Decomposition (DALD), and provide a rigorous convergence proof for its standard version. To…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is…

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…

Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…