IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v76y2020i4d10.1007_s10898-019-00826-6.html
   My bibliography  Save this article

Accelerated iterative hard thresholding algorithm for $$l_0$$l0 regularized regression problem

Author

Listed:
  • Fan Wu

    (Harbin Institute of Technology)

  • Wei Bian

    (Harbin Institute of Technology)

Abstract

In this paper, we propose an accelerated iterative hard thresholding algorithm for solving the $$l_0$$l0 regularized box constrained regression problem. We substantiate that there exists a threshold, if the extrapolation coefficients are chosen below this threshold, the proposed algorithm is equivalent to the accelerated proximal gradient algorithm for solving a corresponding constrained convex problem after finite iterations. Under some proper conditions, we get that the sequence generated by the proposed algorithm is convergent to a local minimizer of the $$l_0$$l0 regularized problem, which satisfies a desired lower bound. Moreover, when the data fitting function satisfies the error bound condition, we prove that both the iterate sequence and the corresponding sequence of objective function values are R-linearly convergent. Finally, we use several numerical experiments to verify our theoretical results.

Suggested Citation

  • Fan Wu & Wei Bian, 2020. "Accelerated iterative hard thresholding algorithm for $$l_0$$l0 regularized regression problem," Journal of Global Optimization, Springer, vol. 76(4), pages 819-840, April.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00826-6
    DOI: 10.1007/s10898-019-00826-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-019-00826-6
    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/s10898-019-00826-6?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. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. Paul Tseng & Sangwoon Yun, 2010. "A coordinate gradient descent method for linearly constrained smooth optimization and support vector machines training," Computational Optimization and Applications, Springer, vol. 47(2), pages 179-206, October.
    4. Wei Bian & Xiaojun Chen, 2017. "Optimality and Complexity for Constrained Optimization Problems with Nonconvex Regularization," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1063-1084, November.
    5. Zhi-Quan Luo & Paul Tseng, 1993. "On the Convergence Rate of Dual Ascent Methods for Linearly Constrained Convex Minimization," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 846-867, November.
    6. Zemin Zheng & Yingying Fan & Jinchi Lv, 2014. "High dimensional thresholded regression and shrinkage effect," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 627-649, June.
    7. Le Thi, H.A. & Pham Dinh, T. & Le, H.M. & Vo, X.T., 2015. "DC approximation approaches for sparse optimization," European Journal of Operational Research, Elsevier, vol. 244(1), pages 26-46.
    8. Hui Zhang & Wotao Yin & Lizhi Cheng, 2015. "Necessary and Sufficient Conditions of Solution Uniqueness in 1-Norm Minimization," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 109-122, January.
    9. Patrick R. Johnstone & Pierre Moulin, 2017. "Local and global convergence of a general inertial proximal splitting scheme for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 67(2), pages 259-292, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    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. 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.
    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. Zhongming Wu & Chongshou Li & Min Li & Andrew Lim, 2021. "Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 79(3), pages 617-644, March.
    4. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.
    5. Luke Mosley & Idris A. Eckley & Alex Gibberd, 2022. "Sparse temporal disaggregation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2203-2233, October.
    6. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.
    7. Hoai An Le Thi & Manh Cuong Nguyen, 2017. "DCA based algorithms for feature selection in multi-class support vector machine," Annals of Operations Research, Springer, vol. 249(1), pages 273-300, February.
    8. Tianxiang Liu & Ting Kei Pong, 2017. "Further properties of the forward–backward envelope with applications to difference-of-convex programming," Computational Optimization and Applications, Springer, vol. 67(3), pages 489-520, July.
    9. Yakui Huang & Hongwei Liu, 2016. "Smoothing projected Barzilai–Borwein method for constrained non-Lipschitz optimization," Computational Optimization and Applications, Springer, vol. 65(3), pages 671-698, December.
    10. A. Chudik & G. Kapetanios & M. Hashem Pesaran, 2018. "A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High‐Dimensional Linear Regression Models," Econometrica, Econometric Society, vol. 86(4), pages 1479-1512, July.
    11. Alexander Chudik & George Kapetanios & M. Hashem Pesaran, 2016. "Big data analytics: a new perspective," Globalization Institute Working Papers 268, Federal Reserve Bank of Dallas.
    12. Xian Zhang & Dingtao Peng, 2022. "Solving constrained nonsmooth group sparse optimization via group Capped- $$\ell _1$$ ℓ 1 relaxation and group smoothing proximal gradient algorithm," Computational Optimization and Applications, Springer, vol. 83(3), pages 801-844, December.
    13. Peili Li & Min Liu & Zhou Yu, 2023. "A global two-stage algorithm for non-convex penalized high-dimensional linear regression problems," Computational Statistics, Springer, vol. 38(2), pages 871-898, June.
    14. Jian Huang & Yuling Jiao & Lican Kang & Jin Liu & Yanyan Liu & Xiliang Lu, 2022. "GSDAR: a fast Newton algorithm for $$\ell _0$$ ℓ 0 regularized generalized linear models with statistical guarantee," Computational Statistics, Springer, vol. 37(1), pages 507-533, March.
    15. Lian, Heng & Kim, Yongdai, 2016. "Nonconvex penalized reduced rank regression and its oracle properties in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 383-393.
    16. Hao Wang & Hao Zeng & Jiashan Wang, 2022. "An extrapolated iteratively reweighted $$\ell _1$$ ℓ 1 method with complexity analysis," Computational Optimization and Applications, Springer, vol. 83(3), pages 967-997, December.
    17. Dewei Zhang & Yin Liu & Sam Davanloo Tajbakhsh, 2022. "A First-Order Optimization Algorithm for Statistical Learning with Hierarchical Sparsity Structure," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1126-1140, March.
    18. Zemin Zheng & Jinchi Lv & Wei Lin, 2021. "Nonsparse Learning with Latent Variables," Operations Research, INFORMS, vol. 69(1), pages 346-359, January.
    19. Miju Ahn, 2020. "Consistency bounds and support recovery of d-stationary solutions of sparse sample average approximations," Journal of Global Optimization, Springer, vol. 78(3), pages 397-422, November.
    20. Patrick R. Johnstone & Pierre Moulin, 2017. "Local and global convergence of a general inertial proximal splitting scheme for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 67(2), pages 259-292, June.

    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_s10898-019-00826-6. 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.