linearized – Optimization Online

Optimal Linearized Alternating Direction Method of Multipliers for Convex Programming

Published: 2017/09/27, Updated: 2017/10/15

Convex Optimization alternating direction method of multipliers, convergence rate, convex optimization, linearized, optimal step size, proximal regularization

The alternating direction method of multipliers (ADMM) is being widely used in a variety of areas; its different variants tailored for different application scenarios have also been deeply researched in the literature. Among them, the linearized ADMM has received particularly wide attention from many areas because of its efficiency and easy implementation. To theoretically guarantee … Read more

Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization

Published: 2010/02/04, Updated: 2011/05/06

Junfeng Yang

Xiao-Ming Yuan

Convex Optimization alternating direction method, augmented lagrangian method, convex optimization, linearized, low rank, nuclear norm

The nuclear norm is widely used to induce low-rank solutions for many optimization problems with matrix variables. Recently, it has been shown that the augmented Lagrangian method (ALM) and the alternating direction method (ADM) are very efficient for many convex programming problems arising from various applications, provided that the resulting subproblems are sufficiently simple to … Read more