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Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…
Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…
By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known…
In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this…
Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…
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…
In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the…
The Strong Constraint 4D Variational (SC-4DVAR) data assimilation method is widely used in climate and weather applications. SC-4DVAR involves solving a minimization problem to compute the maximum a posteriori estimate, which we tackle…
Collaborative transportation of heavy payloads via loco-manipulation is a challenging yet essential capability for legged robots operating in complex, unstructured environments. Centralized planning methods, e.g., holistic trajectory…
Quantization of the parameters of machine learning models, such as deep neural networks, requires solving constrained optimization problems, where the constraint set is formed by the Cartesian product of many simple discrete sets. For such…
Accompanied with the rising popularity of compressed sensing, the Alternating Direction Method of Multipliers (ADMM) has become the most widely used solver for linearly constrained convex problems with separable objectives. In this work, we…
We present a flexible Alternating Direction Method of Multipliers (F-ADMM) algorithm for solving optimization problems involving a strongly convex objective function that is separable into $n \geq 2$ blocks, subject to (non-separable)…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
The 4D-Var method for filtering partially observed nonlinear chaotic dynamical systems consists of finding the maximum a-posteriori (MAP) estimator of the initial condition of the system given observations over a time window, and…
This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order…
Multi-agent distributed consensus optimization problems arise in many signal processing applications. Recently, the alternating direction method of multipliers (ADMM) has been used for solving this family of problems. ADMM based distributed…
In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the…
Hyperspectral imagery collected from airborne or satellite sources inevitably suffers from spectral variability, making it difficult for spectral unmixing to accurately estimate abundance maps. The classical unmixing model, the linear…
The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth…
In this paper, a generic extension of variational mode decomposition (VMD) algorithm for multivariate or multichannel data sets is presented. We first define a model for multivariate modulated oscillations that is based on the presence of a…