Related papers: Network Lasso: Clustering and Optimization in Larg…
We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have…
Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal.…
Graph-structured combinatorial problems in complex networks are prevalent in many domains, and are computationally demanding due to their complexity and non-linear nature. Traditional evolutionary algorithms (EAs), while robust, often face…
The group Lasso is an extension of the Lasso for feature selection on (predefined) non-overlapping groups of features. The non-overlapping group structure limits its applicability in practice. There have been several recent attempts to…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
In neuroscience, researchers seek to uncover the connectivity of neurons from large-scale neural recordings or imaging; often people employ graphical model selection and estimation techniques for this purpose. But, existing technologies can…
Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the…
While traditional Deep Learning (DL) optimization methods treat all training samples equally, Distributionally Robust Optimization (DRO) adaptively assigns importance weights to different samples. However, a significant gap exists between…
A recently proposed learning algorithm for massive network-structured data sets (big data over networks) is the network Lasso (nLasso), which extends the well- known Lasso estimator from sparse models to network-structured datasets.…
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…
In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for solving large scale convex optimization problems with…
We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve $L_1$/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of…
Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
As problems in machine learning, smartgrid dispatch, and IoT coordination problems have grown, distributed and fully-decentralized optimization models have gained attention for providing computational scalability to optimization tools.…
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…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
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…