-

 

 

 




Optimization Online





 

A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

Chang Xiaokai (15293183303***at***163.com)
Liu Sanyang (liusanyang***at***126.com)
Zhao Pengjun (846188043***at***qq.com)
Song Dunjiang (songdj***at***casisd.cn)

Abstract: The linearized alternating direction method of multipliers (ADMM), with indefinite proximal regularization, has been proved to be efficient for solving separable convex optimization subject to linear constraints. In this paper, we present a generalization of linearized ADMM (G-LADMM) to solve two-block separable convex minimization model, which linearizes all the subproblems by choosing a proper positive-definite or indefinite proximal term and updates the Lagrangian multiplier twice in different ways. Furthermore, the proposed G-LADMM can be expressed as a proximal point algorithm (PPA), and all the subproblems are just to estimate the proximity operator of the function in the objective. We specify the domain of the proximal parameter and stepsizes to guarantee that G-LADMM is globally convergent. It turns out that our convergence domain of the proximal parameter and stepsizes is significantly larger than other con- vergence domains in the literature. The numerical experiments illustrate the improvements of the proposed G-LADMM to solve LASSO and image decomposition problems.

Keywords: alternating direction method of multipliers proximal point algorithm separable convex programming linearization indefinite proximal regularization LASSO

Category 1: Convex and Nonsmooth Optimization

Citation: Xiaokai Chang,Sanyang Liu,Pengjun Zhao, Dunjiang Song, A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming, Journal of Computational and Applied Mathematics, 2019

Download: [PDF]

Entry Submitted: 12/12/2018
Entry Accepted: 12/12/2018
Entry Last Modified: 02/19/2019

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society