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A new alternating direction method for linearly constrained nonconvex optimization problems

Author

Listed:
  • X. Wang
  • S. Li
  • X. Kou
  • Q. Zhang

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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • X. Wang & S. Li & X. Kou & Q. Zhang, 2015. "A new alternating direction method for linearly constrained nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 62(4), pages 695-709, August.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:4:p:695-709
    DOI: 10.1007/s10898-015-0268-5
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    References listed on IDEAS

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    1. Dan Xue & Wenyu Sun & Liqun Qi, 2014. "An alternating structured trust region algorithm for separable optimization problems with nonconvex constraints," Computational Optimization and Applications, Springer, vol. 57(2), pages 365-386, March.
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    4. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
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