IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v76y2020i4d10.1007_s10898-019-00830-w.html
   My bibliography  Save this article

An active set Barzilar–Borwein algorithm for $$l_{0}$$l0 regularized optimization

Author

Listed:
  • Wanyou Cheng

    (Dongguan University of Technology)

  • Zixin Chen

    (Dongguan University of Technology)

  • Qingjie Hu

    (Guilin University of Electronic Technology)

Abstract

In this paper, we develop an active set identification technique for the $$\ell _0$$ℓ0 regularization optimization. Such a technique has a strong ability to identify the zero components in a neighbourhood of a strict L-stationary point. Based on the identification technique, we propose an active set Barzilar–Borwein algorithm and prove that any limit point of the sequence generated by the algorithm is a strong stationary point. Some preliminary numerical results are provided, showing that the method is promising.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00830-w
    DOI: 10.1007/s10898-019-00830-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-019-00830-w
    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/s10898-019-00830-w?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. 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.
    2. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    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.
    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. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    2. 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.
    3. Luoying Yang & Tong Tong Wu, 2023. "Model‐based clustering of high‐dimensional longitudinal data via regularization," Biometrics, The International Biometric Society, vol. 79(2), pages 761-774, June.
    4. 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.
    5. 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.
    6. 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.
    7. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    8. 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.
    9. Min Tao & Jiang-Ning Li, 2023. "Error Bound and Isocost Imply Linear Convergence of DCA-Based Algorithms to D-Stationarity," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 205-232, April.
    10. Abhik Ghosh & Magne Thoresen, 2018. "Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 179-210, April.
    11. Jan Pablo Burgard & Joscha Krause & Dennis Kreber & Domingo Morales, 2021. "The generalized equivalence of regularization and min–max robustification in linear mixed models," Statistical Papers, Springer, vol. 62(6), pages 2857-2883, December.
    12. Mingrui Zhong & Zanhua Yin & Zhichao Wang, 2023. "Variable Selection for Sparse Logistic Regression with Grouped Variables," Mathematics, MDPI, vol. 11(24), pages 1-21, December.
    13. Xie Xiaodong & Zheng Shaozhi, 2017. "Group MCP for Cox Models with Time-Varying Coefficients," Journal of Systems Science and Information, De Gruyter, vol. 4(5), pages 476-488, October.
    14. Tianxiang Liu & Akiko Takeda, 2022. "An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems," Computational Optimization and Applications, Springer, vol. 82(1), pages 141-173, May.
    15. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    16. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    17. Emmanouil Androulakis & Christos Koukouvinos & Kalliopi Mylona & Filia Vonta, 2010. "A real survival analysis application via variable selection methods for Cox's proportional hazards model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1399-1406.
    18. Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
    19. Gerhard Tutz & Moritz Berger, 2018. "Tree-structured modelling of categorical predictors in generalized additive regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 737-758, September.
    20. Chenchuan (Mark) Li & Ulrich K. Müller, 2021. "Linear regression with many controls of limited explanatory power," Quantitative Economics, Econometric Society, vol. 12(2), pages 405-442, May.

    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:76:y:2020:i:4:d:10.1007_s10898-019-00830-w. 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.