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An inexact alternating direction method of multipliers with relative error criteria

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Abstract

In this paper, we study an inexact version of the alternating direction method of multipliers (ADMM) for solving two-block separable linearly constrained convex optimization problems. Specifically, the two subproblems in the classic ADMM are allowed to be solved inexactly by certain relative error criteria, in the sense that only two parameters are needed to control the inexactness. Related convergence analysis are established under the assumption that the solution set to the KKT system of the problem is not empty. Numerical results on solving a class of sparse signal recovery problems are also provided to demonstrate the efficiency of the proposed algorithm.

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Notes

  1. https://web.stanford.edu/~boyd/papers/admm/lasso/lasso.html.

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Acknowledgments

We are very grateful to the anonymous referees for their valuable comments and suggestions. We also want to thank Mr. Liang Chen at Hunan University for many useful comments. This work was supported by the National Natural Science Foundation of China (Grant No. 11271117).

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Jiaxin Xie, Anping Liao & Xiaobo Yang

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  1. Jiaxin Xie
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  2. Anping Liao
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  3. Xiaobo Yang
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Correspondence to Anping Liao.

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Xie, J., Liao, A. & Yang, X. An inexact alternating direction method of multipliers with relative error criteria. Optim Lett 11, 583–596 (2017). https://doi.org/10.1007/s11590-016-1021-9

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