Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables

Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables

The alternating direction method of multipliers (ADMM) has been widely explored due to its broad applications, and its convergence has been gotten in the real field. In this paper, an ADMM is presented for separable convex optimization of real functions in complex variables. First, the convergence o...

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Main Authors: Lu Li, Xingyu Wang, Guoqiang Wang
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/104531
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spelling doaj-edc47673e82a46e9a08d4f9d7b0aae842020-11-25T00:45:17ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/104531104531Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex VariablesLu Li0Xingyu Wang1Guoqiang Wang2School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, ChinaSchool of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, ChinaCollege of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, ChinaThe alternating direction method of multipliers (ADMM) has been widely explored due to its broad applications, and its convergence has been gotten in the real field. In this paper, an ADMM is presented for separable convex optimization of real functions in complex variables. First, the convergence of the proposed method in the complex domain is established by using the Wirtinger Calculus technique. Second, the basis pursuit (BP) algorithm is given in the form of ADMM in which the projection algorithm and the soft thresholding formula are generalized from the real case. The numerical simulations on the reconstruction of electroencephalogram (EEG) signal are provided to show that our new ADMM has better behavior than the classic ADMM for solving separable convex optimization of real functions in complex variables.http://dx.doi.org/10.1155/2015/104531
collection DOAJ
language English
format Article
sources DOAJ
author Lu Li
Xingyu Wang
Guoqiang Wang
spellingShingle Lu Li
Xingyu Wang
Guoqiang Wang
Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables
Mathematical Problems in Engineering
author_facet Lu Li
Xingyu Wang
Guoqiang Wang
author_sort Lu Li
title Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables
title_short Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables
title_full Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables
title_fullStr Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables
title_full_unstemmed Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables
title_sort alternating direction method of multipliers for separable convex optimization of real functions in complex variables
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description The alternating direction method of multipliers (ADMM) has been widely explored due to its broad applications, and its convergence has been gotten in the real field. In this paper, an ADMM is presented for separable convex optimization of real functions in complex variables. First, the convergence of the proposed method in the complex domain is established by using the Wirtinger Calculus technique. Second, the basis pursuit (BP) algorithm is given in the form of ADMM in which the projection algorithm and the soft thresholding formula are generalized from the real case. The numerical simulations on the reconstruction of electroencephalogram (EEG) signal are provided to show that our new ADMM has better behavior than the classic ADMM for solving separable convex optimization of real functions in complex variables.
url http://dx.doi.org/10.1155/2015/104531
work_keys_str_mv AT luli alternatingdirectionmethodofmultipliersforseparableconvexoptimizationofrealfunctionsincomplexvariables
AT xingyuwang alternatingdirectionmethodofmultipliersforseparableconvexoptimizationofrealfunctionsincomplexvariables
AT guoqiangwang alternatingdirectionmethodofmultipliersforseparableconvexoptimizationofrealfunctionsincomplexvariables
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