Related papers: A Hypergraph-Partitioned Vertex Programming Approa…
We study a class of structured convex optimization problems, which have a two-block separable objective and nonlinear functional constraints as well as affine constraints that couple the two block variables. Such problems naturally arise…
A lift-and-permute scheme of alternating direction method of multipliers (ADMM) is proposed for linearly constrained convex programming. It contains not only the newly developed balanced augmented Lagrangian method and its dual-primal…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
Big data, including applications with high security requirements, are often collected and stored on multiple heterogeneous devices, such as mobile devices, drones and vehicles. Due to the limitations of communication costs and security…
In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data…
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…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…
This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…
We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic…
Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…
This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…
Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require…
In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear…
We investigate a class of general combinatorial graph problems, including MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints and solved via the alternating direction method of multipliers…
We investigate a class of general combinatorial graph problems, including MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints and solved via the alternating direction method of multipliers…
We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…
We introduce Wasserstein consensus alternating direction method of multipliers (ADMM) and its entropic-regularized version: Sinkhorn consensus ADMM, to solve measure-valued optimization problems with convex additive objectives. Several…
When solving consensus optimization problems over a graph, there is often an explicit characterization of the convergence rate of Gradient Descent (GD) using the spectrum of the graph Laplacian. The same type of problems under the…
In this paper, we propose a generalized alternating direction method of multipliers (ADMM) with semi-proximal terms for solving a class of convex composite conic optimization problems, of which some are high-dimensional, to moderate…