Related papers: Augmented Lagrangian Method for Constrained Nuclea…

We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method features an easily implementable rule not only for updating the penalty parameters, but also for…

Density Functional Theory (DFT) is a pivotal method within quantum chemistry and materials science, with its core involving the construction and solution of the Kohn-Sham Hamiltonian. Despite its importance, the application of DFT is…

In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and…

The convergence of the effective field theory (EFT) approach of Furnstahl, Serot and Tang to the nuclear many-body problem is studied by applying it to selected doubly-magic nuclei far from stability. An independently developed code, which…

In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated…

A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by…

We study policy optimization for infinite-horizon, discounted constrained Markov decision processes (CMDPs). While existing theoretical guarantees typically hold for the mixture policy, deploying such a policy is computationally and memory…

A lift-and-permute scheme of alternating direction method of multipliers (ADMM) is proposed for linearly constrained convex programming. It contains not only the newly developed balanced augmented Lagrangian method and its dual-primal…

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…

Square-root Lasso problems are proven robust regression problems. Furthermore, square-root regression problems with structured sparsity also plays an important role in statistics and machine learning. In this paper, we focus on the…

Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of…

Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In…

An arbitrary Lagrangian--Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane…

Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…

Two types of approaches to modeling molecular systems have demonstrated high practical efficiency. Density functional theory (DFT), the most widely used quantum chemical method, is a physical approach predicting energies and electron…

We analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the augmented Lagrangian function value is…

This work continues a program to systematically generalize the Skyrme Hartree-Fock method for medium and heavy nuclei by applying effective field theory (EFT) methods to Kohn-Sham density functional theory (DFT). When conventional Kohn-Sham…

This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…

We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a…

This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more…