Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

An alternating direction-based contraction method for linearly constrained separable convex programming problems

Language

English

Abstract

The classical alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming and variational inequalities where the involved operator is formed as the sum of two individual functions without crossed variables. Recently, ADM has found many novel applications in diversified areas, such as image processing and statistics. However, it is still not clear whether ADM can be extended to the case where the operator is the sum of more than two individual functions. In this article, we extend the spirit of ADM to solve the general case of the linearly constrained separable convex programming problems whose involved operator is separable into finitely many individual functions. As a result, an alternating direction-based contraction-type method is developed. The realization of tackling this class of problems broadens the applicable scope of ADM substantially. © 2013 Copyright Taylor and Francis Group, LLC.

Keywords

alternating direction method, contraction method, convex programming, linear constraint, separable structure

Publication Date

2013

Source Publication Title

Optimization

Volume

62

Issue

4

Start Page

573

End Page

596

Publisher

Taylor & Francis

DOI

10.1080/02331934.2011.611885

ISSN (print)

02331934

ISSN (electronic)

10294945

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