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A proximal alternating direction method of multipliers for a minimization problem with nonconvex constraints

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  • Zheng Peng
  • Jianli Chen
  • Wenxing Zhu

Abstract

In this paper, a proximal alternating direction method of multipliers is proposed for solving a minimization problem with Lipschitz nonconvex constraints. Such problems are raised in many engineering fields, such as the analytical global placement of very large scale integrated circuit design. The proposed method is essentially a new application of the classical proximal alternating direction method of multipliers. We prove that, under some suitable conditions, any subsequence of the sequence generated by the proposed method globally converges to a Karush–Kuhn–Tucker point of the problem. We also present a practical implementation of the method using a certain self-adaptive rule of the proximal parameters. The proposed method is used as a global placement method in a placer of very large scale integrated circuit design. Preliminary numerical results indicate that, compared with some state-of-the-art global placement methods, the proposed method is applicable and efficient. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Zheng Peng & Jianli Chen & Wenxing Zhu, 2015. "A proximal alternating direction method of multipliers for a minimization problem with nonconvex constraints," Journal of Global Optimization, Springer, vol. 62(4), pages 711-728, August.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:4:p:711-728
    DOI: 10.1007/s10898-015-0287-2
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    References listed on IDEAS

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    1. Xiaoming Yuan, 2011. "An improved proximal alternating direction method for monotone variational inequalities with separable structure," Computational Optimization and Applications, Springer, vol. 49(1), pages 17-29, May.
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    Cited by:

    1. Dolgopolik, Maksim V., 2021. "The alternating direction method of multipliers for finding the distance between ellipsoids," Applied Mathematics and Computation, Elsevier, vol. 409(C).

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