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A Note on the Alternating Direction Method of Multipliers

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Abstract

We consider the linearly constrained separable convex programming, whose objective function is separable into m individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case m=2, while it remains open whether its convergence can be extended to the general case m≥3. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.

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Acknowledgements

The research was supported by the National Natural Science Foundation of China (NSFC) grants 11071122, 11171159, Doctoral Found of Ministry of Education of China 20103207110002, and the Hong Kong General Research Grant: HKBU203311.

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Authors and Affiliations

  1. School of Mathematical Science and Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing, 210046, P.R. China

    Deren Han

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China

    Xiaoming Yuan

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  1. Deren Han
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  2. Xiaoming Yuan
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Correspondence to Xiaoming Yuan.

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Han, D., Yuan, X. A Note on the Alternating Direction Method of Multipliers. J Optim Theory Appl 155, 227–238 (2012). https://doi.org/10.1007/s10957-012-0003-z

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  • DOI: https://doi.org/10.1007/s10957-012-0003-z

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