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A new alternating direction method for linearly constrained nonconvex optimization problems

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Abstract

In this paper, we study the classical nonconvex linearly constrained optimization problem. Under some mild conditions, we obtain that the penalization sequence is nonincreasing and the sequence generated by our algorithm has finite length. Based on the assumption that the objective functions have Kurdyka–Lojasiewicz property, we prove the convergence of the algorithm. We also show the numerical efficiency of our method by the concrete applications in the areas of image processing and statistics.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grants number: 11171362, 11301567 and 11401058), Specialized Research Fund for the Doctoral Program of Higher Education (Grant number: 20120191110031), the Technology Project of Chongqing Education Committee (Grant number: KJ130732), and the Research Start Project of Chongqing Technology and Business University (Grant number: 2012-56-04). The authors thank the anonymous reviewers for their valuable comments and suggestions, which helped to improve the paper.

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  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    X. Y. Wang, S. J. Li, X. P. Kou & Q. F. Zhang

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  1. X. Y. Wang
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  2. S. J. Li
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  3. X. P. Kou
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Correspondence to S. J. Li.

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Wang, X.Y., Li, S.J., Kou, X.P. et al. A new alternating direction method for linearly constrained nonconvex optimization problems. J Glob Optim 62, 695–709 (2015). https://doi.org/10.1007/s10898-015-0268-5

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  • DOI: https://doi.org/10.1007/s10898-015-0268-5

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