Communications in Mathematical Sciences

Volume 13 (2015)

Number 1

A dual algorithm for a class of augmented convex signal recovery models

Pages: 103 – 112

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n1.a5

Authors

Hui Zhang (Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, Hunan, China)

Lizhi Cheng (State Key Laboratory for High Performance Computation, and Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, Hunan, China)

Wotao Yin (Department of Mathematics, University of California at Los Angeles)

Abstract

Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient algorithm. The proposed algorithm includes the linearized Bregman algorithm and the singular value thresholding algorithm as special cases. Based on fundamental properties of proximal operators, we present a concise approach to establish the convergence of both primal and dual sequences, improving the results in the existing literature. Extensions to models with gauge functions are provided.

Keywords

augmented convex model, Lagrange dual, primal-dual, proximal operator, gauge, signal recovery

2010 Mathematics Subject Classification

65F22, 65K05

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Published 16 July 2014