IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v85y2023i4d10.1007_s10898-022-01239-8.html
   My bibliography  Save this article

Calmness of partial perturbation to composite rank constraint systems and its applications

Author

Listed:
  • Yitian Qian

    (South China University of Technology)

  • Shaohua Pan

    (South China University of Technology)

  • Yulan Liu

    (Guangdong University of Technology)

Abstract

This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type error bound and also a global Lipschitz-type error bound under a certain compactness. Based on its lifted formulation, we derive two criteria for identifying those closed sets such that the associated partial perturbation possesses the calmness, and provide a collection of examples to demonstrate that the criteria are satisfied by common nonnegative and positive semidefinite rank constraint sets. Then, we use the calmness of this perturbation to obtain several global exact penalties for rank constrained optimization problems, and a family of equivalent DC surrogates for rank regularized problems.

Suggested Citation

  • Yitian Qian & Shaohua Pan & Yulan Liu, 2023. "Calmness of partial perturbation to composite rank constraint systems and its applications," Journal of Global Optimization, Springer, vol. 85(4), pages 867-889, April.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:4:d:10.1007_s10898-022-01239-8
    DOI: 10.1007/s10898-022-01239-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01239-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-022-01239-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 649-662.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Xinrong Li & Naihua Xiu & Shenglong Zhou, 2020. "Matrix Optimization Over Low-Rank Spectral Sets: Stationary Points and Local and Global Minimizers," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 895-930, March.
    5. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
    6. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    7. Zhuoxuan Jiang & Xinyuan Zhao & Chao Ding, 2021. "A proximal DC approach for quadratic assignment problem," Computational Optimization and Applications, Springer, vol. 78(3), pages 825-851, April.
    8. Yulan Liu & Shujun Bi & Shaohua Pan, 2018. "Equivalent Lipschitz surrogates for zero-norm and rank optimization problems," Journal of Global Optimization, Springer, vol. 72(4), pages 679-704, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dongdong Zhang & Shaohua Pan & Shujun Bi & Defeng Sun, 2023. "Zero-norm regularized problems: equivalent surrogates, proximal MM method and statistical error bound," Computational Optimization and Applications, Springer, vol. 86(2), pages 627-667, November.
    2. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    3. Yulan Liu & Shujun Bi & Shaohua Pan, 2018. "Equivalent Lipschitz surrogates for zero-norm and rank optimization problems," Journal of Global Optimization, Springer, vol. 72(4), pages 679-704, December.
    4. Bo Jiang & Tianyi Lin & Shiqian Ma & Shuzhong Zhang, 2019. "Structured nonconvex and nonsmooth optimization: algorithms and iteration complexity analysis," Computational Optimization and Applications, Springer, vol. 72(1), pages 115-157, January.
    5. Wenxing Zhu & Huating Huang & Lanfan Jiang & Jianli Chen, 0. "Weighted thresholding homotopy method for sparsity constrained optimization," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-29.
    6. Liu, Jingjing & Ma, Ruijie & Zeng, Xiaoyang & Liu, Wanquan & Wang, Mingyu & Chen, Hui, 2021. "An efficient non-convex total variation approach for image deblurring and denoising," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    7. Min Li & Zhongming Wu, 2019. "Convergence Analysis of the Generalized Splitting Methods for a Class of Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 535-565, November.
    8. Bo Wen & Xiaojun Chen & Ting Kei Pong, 2018. "A proximal difference-of-convex algorithm with extrapolation," Computational Optimization and Applications, Springer, vol. 69(2), pages 297-324, March.
    9. Abbaszadehpeivasti, Hadi, 2024. "Performance analysis of optimization methods for machine learning," Other publications TiSEM 3050a62d-1a1f-494e-99ef-7, Tilburg University, School of Economics and Management.
    10. Tianxiang Liu & Ting Kei Pong & Akiko Takeda, 2019. "A refined convergence analysis of $$\hbox {pDCA}_{e}$$ pDCA e with applications to simultaneous sparse recovery and outlier detection," Computational Optimization and Applications, Springer, vol. 73(1), pages 69-100, May.
    11. Yitian Qian & Shaohua Pan & Shujun Bi, 2023. "A matrix nonconvex relaxation approach to unconstrained binary polynomial programs," Computational Optimization and Applications, Springer, vol. 84(3), pages 875-919, April.
    12. Wenxing Zhu & Huating Huang & Lanfan Jiang & Jianli Chen, 2022. "Weighted thresholding homotopy method for sparsity constrained optimization," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1924-1952, October.
    13. Zhili Ge & Zhongming Wu & Xin Zhang & Qin Ni, 2023. "An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 821-844, August.
    14. Guoyin Li & Tianxiang Liu & Ting Kei Pong, 2017. "Peaceman–Rachford splitting for a class of nonconvex optimization problems," Computational Optimization and Applications, Springer, vol. 68(2), pages 407-436, November.
    15. Wanyou Cheng & Zixin Chen & Qingjie Hu, 2020. "An active set Barzilar–Borwein algorithm for $$l_{0}$$l0 regularized optimization," Journal of Global Optimization, Springer, vol. 76(4), pages 769-791, April.
    16. Peiran Yu & Ting Kei Pong, 2019. "Iteratively reweighted $$\ell _1$$ ℓ 1 algorithms with extrapolation," Computational Optimization and Applications, Springer, vol. 73(2), pages 353-386, June.
    17. Ning Zhang & Jin Yang, 2023. "Sparse precision matrix estimation with missing observations," Computational Statistics, Springer, vol. 38(3), pages 1337-1355, September.
    18. Lei Yang, 2024. "Proximal Gradient Method with Extrapolation and Line Search for a Class of Non-convex and Non-smooth Problems," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 68-103, January.
    19. Tao Sun & Hao Jiang & Lizhi Cheng, 2017. "Global convergence of proximal iteratively reweighted algorithm," Journal of Global Optimization, Springer, vol. 68(4), pages 815-826, August.
    20. Yue Xie & Uday V. Shanbhag, 2021. "Tractable ADMM schemes for computing KKT points and local minimizers for $$\ell _0$$ ℓ 0 -minimization problems," Computational Optimization and Applications, Springer, vol. 78(1), pages 43-85, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:85:y:2023:i:4:d:10.1007_s10898-022-01239-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.