Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

An ADM-based splitting method for separable convex programming

Language

English

Abstract

We consider the convex minimization problem with linear constraints and a block-separable objective function which is represented as the sum of three functions without coupled variables. To solve this model, it is empirically effective to extend straightforwardly the alternating direction method of multipliers (ADM for short). But, the convergence of this straightforward extension of ADM is still not proved theoretically. Based on ADM's straightforward extension, this paper presents a new splitting method for the model under consideration, which is empirically competitive to the straightforward extension of ADM and meanwhile the global convergence can be proved under standard assumptions. At each iteration, the new method corrects the output of the straightforward extension of ADM by some slight correction computation to generate a new iterate. Thus, the implementation of the new method is almost as easy as that of ADM's straightforward extension. We show the numerical efficiency of the new method by some applications in the areas of image processing and statistics. © 2012 Springer Science+Business Media New York.

Keywords

Alternating direction method of multipliers, Block-separable, Convex minimization, Global convergence, Operator splitting methods

Publication Date

2013

Source Publication Title

Computational Optimization and Applications

Volume

54

Issue

2

Start Page

343

End Page

369

Publisher

Springer

DOI

10.1007/s10589-012-9510-y

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10589-012-9510-y

ISSN (print)

09266003

ISSN (electronic)

15732894

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