Related papers: Linear Convergence Rate of a Class of Distributed …
We propose a distributed, cubic-regularized Newton method for large-scale convex optimization over networks. The proposed method requires only local computations and communications and is suitable for federated learning applications over…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all…
We consider the augmented Lagrangian method (ALM) as a solver for the fused lasso signal approximator (FLSA) problem. The ALM is a dual method in which squares of the constraint functions are added as penalties to the Lagrangian. In order…
We study distributed optimization problems when $N$ nodes minimize the sum of their individual costs subject to a common vector variable. The costs are convex, have Lipschitz continuous gradient (with constant $L$), and bounded gradient. We…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…
The augmented Lagrangian method (ALM) has gained tremendous popularity for its elegant theory and impressive numerical performance since it was proposed by Hestenes and Powell in 1969. It has been widely used in numerous efficient solvers…
We study a standard distributed optimization framework where $N$ networked nodes collaboratively minimize the sum of their local convex costs. The main body of existing work considers the described problem when the underling network is…
This paper presents a distributed optimization scheme over a network of agents in the presence of cost uncertainties and over switching communication topologies. Inspired by recent advances in distributed convex optimization, we propose a…
We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between…
In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a…
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…
In this work, we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function, a set of affine equality constraints, and a set of convex inequality constraints. We propose a…
We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the…
This paper examines online distributed Alternating Direction Method of Multipliers (ADMM). The goal is to distributively optimize a global objective function over a network of decision makers under linear constraints. The global objective…
Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…