An inertial proximal alternating direction method of multipliers for nonconvex optimization

The alternating direction method of multipliers (ADMM) is an efficient method for solving separable problems. However, ADMM may not converge when there is a nonconvex function in the objective. The main contributions of this paper are proposing and analysing an inertial proximal ADMM for a class of...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 98; no. 6; pp. 1199 - 1217
Main Authors Chao, M. T., Zhang, Y., Jian, J. B.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.06.2021
Taylor & Francis Ltd
Subjects
Algorithms
Alternating direction method of multipliers
Convergence
inertial proximal point method
Kurdyka-Łojasiewicz property
Multipliers
nonconvex optimization
nonsmooth
Optimization
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ISSN0020-7160
1029-0265
DOI10.1080/00207160.2020.1812585

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Summary:The alternating direction method of multipliers (ADMM) is an efficient method for solving separable problems. However, ADMM may not converge when there is a nonconvex function in the objective. The main contributions of this paper are proposing and analysing an inertial proximal ADMM for a class of nonconvex optimization problems. The proposed algorithm combines the basic ideas of the proximal ADMM and the inertial proximal point method. The global and strong convergence of the proposed algorithm is analysed under mild conditions. Finally, we give some preliminary numerical results to show the effectiveness of the proposed algorithm.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2020.1812585