The Alternating Direction Method of Multipliers (ADMM) is a method that solves convex optimization problems of the form min(f(x) + g(z)) subject to Ax + Bz = c, where A and B are suitable matrices and c is a vector, for optimal points (xopt, zopt). It is commonly used for distributed convex minimization on large scale data-sets. However, it can be technically difficult to implement and there is...

The paper considers computational domains structured as a 3D grid of cells. It presents a cell-to-hypercube map that is useful for implementing the Alternating Direction Method (ADM). The map is shown to be perfectly load-balanced, and to optimally preserve adjacencies between cells in the computational domain.

We consider cooperative distributed model predictive control of a linear, timeinvariant, discrete-time plant, which consists of coupled subsystems. The cooperating controllers minimize a quadratic cost criterion subject to input and state constraints. We outline two approaches for such distributed controllers using the alternating direction multiplier method, which allows to obtain convergence ...

Semi-definite rank minimization problems model a wide range of applications in both signal processing and machine learning fields. This class of problem is NP-hard in general. In this paper, we propose a proximal Alternating Direction Method (ADM) for the well-known semi-definite rank regularized minimization problem. Specifically, we first reformulate this NP-hard problem as an equivalent bico...

We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an alternating direction augmented Lagrangian (ADAL) method, based on a new variable splitting approach that results in subproblems that can be solved efficiently and ...

Matrix completion(MC), which is to recover a data matrix from a sampling of its entries, arises in many applications. In this work, we consider find the solutions of the MC problems by solving a series of fixed rank problems. For the fixed rank problems, variables are divided into two parts naturally based on matrix factorization and a simple alternative direction method framework is proposed. ...

We study regularized stochastic convex optimization subject to linear equality constraints. This class of problems was recently also studied by Ouyang et al. (2013) and Suzuki (2013); both introduced similar stochastic alternating direction method of multipliers (SADMM) algorithms. However, the analysis of both papers led to suboptimal convergence rates. This paper presents two new SADMM method...

We present three new approximate versions of alternating direction method of multipliers (ADMM), all of which require only knowledge of subgradients of the subproblem objectives, rather than bounds on the distance to the exact subproblem solution. One version, which applies only to certain common special cases, is based on combining the operator-splitting analysis of the ADMM with a relative-er...

In this paper we propose three iterative greedy algorithms for compressed sensing, called iterative alternating direction (IAD), normalized iterative alternating direction (NIAD) and alternating direction pursuit (ADP), which stem from the iteration steps of alternating direction method of multiplier (ADMM) for `0-regularized least squares (`0-LS) and can be considered as the alternating direct...

in general plane regions and with respect to linear boundary conditions, is a classical problem of numerical analysis. Many such boundary value problems have been solved successfully on high-speed computing machines, using the (iterative) Young-Frankel "successive overrelaxation" (SOR) method as defined in [l] and [2], and variants thereof ("line" and "block" overrelaxation). For this method, e...