Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Linearized alternating direction method with Gaussian back substitution for separable convex programming

Language

English

Abstract

Recently, we have proposed combining the alternating direction method of multipliers (ADMM) with a Gaussian back substitution procedure for solving the convex minimization model with linear constraints and a general separable objective function, i.e., the objective function is the sum of many functions without coupled variables. In this paper, we further study this topic and show that the decomposed subproblems in the ADMM procedure can be substantially alleviated by linearizing the involved quadratic terms arising from the augmented Lagrangian penalty. When the resolvent operators of the separable functions in the objective have closed-form representations, embedding the linearization into the ADMM subproblems becomes necessary to yield easy subproblems with closed-form solutions. We thus show theoretically that the blend of ADMM, Gaussian back substitution and linearization works effectively for the separable convex minimization model under consideration.

Keywords

Alternating direction method of multipliers, Gaussian back substitution, Linearization, Resolvent operator, Separable convex programming

Publication Date

2013

Source Publication Title

Numerical Algebra, Control and Optimization

Volume

3

Issue

2

Start Page

247

End Page

260

Publisher

American Institute of Mathematical Sciences

DOI

10.3934/naco.2013.3.247

Link to Publisher's Edition

http://dx.doi.org/10.3934/naco.2013.3.247

ISSN (print)

21553289

ISSN (electronic)

21553297

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