Related papers: An Adaptive Parallel Arc-Length Method
The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method, the ALM can satisfy equality constraints in an exact way.…
This paper solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion which avoids linearized approximations altogether. Based on creating virtual synthetic measurements, the algorithm uses a linear time-…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can…
We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent…
We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in parallel. To this end, we partition the data and distribute the resulting subproblems among the available…
Model parallelism is conventionally viewed as a method to scale a single large deep learning model beyond the memory limits of a single device. In this paper, we demonstrate that model parallelism can be additionally used for the…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
The objective of this paper is to design an efficient and convergent alternating direction method of multipliers (ADMM) for finding a solution of medium accuracy to conic programming problems whose constraints consist of linear equalities,…
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…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
The Alternating Direction Method of Multipliers (ADMM) has now days gained tremendous attentions for solving large-scale machine learning and signal processing problems due to the relative simplicity. However, the two-block structure of the…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and…
We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves a sequence of inner subproblems which can be enforced to be strongly convex and which therefore admit a…
In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…
We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the…
Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require…
As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…
As the artificial intelligence community advances into the era of large models with billions of parameters, distributed training and inference have become essential. While various parallelism strategies-data, model, sequence, and…