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This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…
We propose both serial and parallel proximal (linearized) alternating direction method of multipliers (ADMM) algorithms for training residual neural networks. In contrast to backpropagation-based approaches, our methods inherently mitigate…
In this paper, we show that for a class of linearly constrained convex composite optimization problems, an (inexact) symmetric Gauss-Seidel based majorized multi-block proximal alternating direction method of multipliers (ADMM) is…
This paper discusses a consensus-based alternating direction method of multipliers (ADMM) approach to solve the multi-area coordinated network-constrained unit commitment (NCUC) problem in a distributed manner. Due to political and…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
Adaptive gradient-based optimization methods such as \textsc{Adagrad}, \textsc{Rmsprop}, and \textsc{Adam} are widely used in solving large-scale machine learning problems including deep learning. A number of schemes have been proposed in…
This paper introduces the Bi-linear consensus Alternating Direction Method of Multipliers (Bi-cADMM), aimed at solving large-scale regularized Sparse Machine Learning (SML) problems defined over a network of computational nodes.…
The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring radial topology. The growing use of renewable energy and the complexity of managing modern power grids make…
Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…
Distributed optimization is often widely attempted and innovated as an attractive and preferred methodology to solve large-scale problems effectively in a localized and coordinated manner. Thus, it is noteworthy that the methodology of…
This paper presents a numerical solver for computing continuous trajectories in non-convex environments. Our approach relies on a customized implementation of the Alternating Direction Method of Multipliers (ADMM) built upon two key…
Federated systems enable collaborative training on highly heterogeneous data through model personalization, which can be facilitated by employing multi-task learning algorithms. However, significant variation in device computing…
The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and…
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special…
The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…
We consider the consensual distributed optimization problem and propose an asynchronous version of the Alternating Direction Method of Multipliers (ADMM) algorithm to solve it. The `asynchronous' part here refers to the fact that only one…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
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…
This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…