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Network Lasso (NL for short) is a methodology for estimating models by simultaneously clustering data samples and fitting the models to the samples. It often succeeds in forming clusters thanks to the geometry of the $\ell_1$-regularizer…

Federated learning has shown its advances over the last few years but is facing many challenges, such as how algorithms save communication resources, how they reduce computational costs, and whether they converge. To address these issues,…

In this paper, we study a constrained minimization problem that arise from materials science to determine the dislocation (line defect) structure of grain boundaries. The problems aims to minimize the energy of the grain boundary with…

In this work we address the problem of distributed optimization of the sum of convex cost functions in the context of multi-agent systems over lossy communication networks. Building upon operator theory, first, we derive an ADMM-like…

Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priors results in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization…

Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed…

We propose a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions.…

Adversarial attacks pose a major threat to machine learning and to the systems that rely on it. In the cybersecurity domain, adversarial cyber-attack examples capable of evading detection are especially concerning. Nonetheless, an example…

We analyze the performance of the alternating direction method of multipliers (ADMM) to track, in a decentralized manner, a solution of a stochastic sequence of optimization problems parametrized by a discrete time Markov process. The main…

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…

In this paper we propose a distributed implementation of the relaxed Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization of a separable convex cost function, whose terms are stored by a set of interacting agents,…

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…

In this paper, we propose a unified framework of inexact stochastic Alternating Direction Method of Multipliers (ADMM) for solving nonconvex problems subject to linear constraints, whose objective comprises an average of finite-sum smooth…

The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solution pairs, it often enters prolonged slow-convergence…

Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization…

We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design…

In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…

This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…

This University of Rochester Physics Ph.D. dissertation introduces concepts in compressive sensing, quantum entanglement, FMCW LiDAR, and quantum data locking. Additionally, the appendix serves as a thorough reference for those interested…

Community detection has attracted increasing attention during the past decade, and many algorithms have been proposed to find the underlying community structure in a given network. Many of these algorithms are based on modularity…