IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v61y2015i1p79-99.html
   My bibliography  Save this article

On the proximal Landweber Newton method for a class of nonsmooth convex problems

Author

Listed:
  • Hai-Bin Zhang
  • Jiao-Jiao Jiang
  • Yun-Bin Zhao

Abstract

We consider a class of nonsmooth convex optimization problems where the objective function is a convex differentiable function regularized by the sum of the group reproducing kernel norm and $$\ell _1$$ ℓ 1 -norm of the problem variables. This class of problems has many applications in variable selections such as the group LASSO and sparse group LASSO. In this paper, we propose a proximal Landweber Newton method for this class of convex optimization problems, and carry out the convergence and computational complexity analysis for this method. Theoretical analysis and numerical results show that the proposed algorithm is promising. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Hai-Bin Zhang & Jiao-Jiao Jiang & Yun-Bin Zhao, 2015. "On the proximal Landweber Newton method for a class of nonsmooth convex problems," Computational Optimization and Applications, Springer, vol. 61(1), pages 79-99, May.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:1:p:79-99
    DOI: 10.1007/s10589-014-9703-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-014-9703-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-014-9703-7?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. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    2. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    3. Haibin Zhang & Juan Wei & Meixia Li & Jie Zhou & Miantao Chao, 2014. "On proximal gradient method for the convex problems regularized with the group reproducing kernel norm," Journal of Global Optimization, Springer, vol. 58(1), pages 169-188, January.
    4. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    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. 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.
    2. Schaffer, Markus & Vera-Valdés, J. Eduardo & Marszal-Pomianowska, Anna, 2024. "Exploring smart heat meter data: A co-clustering driven approach to analyse the energy use of single-family houses," Applied Energy, Elsevier, vol. 371(C).
    3. Yi Tan & Prakash P. Shenoy & Ben Sherwood & Catherine Shenoy & Melinda Gaddy & Mary E. Oehlert, 2024. "Bayesian Network Models for PTSD Screening in Veterans," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 495-509, March.
    4. Piotr Swierkowski & Adrian Barnett, 2018. "Identification of hospital cost drivers using sparse group lasso," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-19, October.
    5. Silvia Villa & Lorenzo Rosasco & Sofia Mosci & Alessandro Verri, 2014. "Proximal methods for the latent group lasso penalty," Computational Optimization and Applications, Springer, vol. 58(2), pages 381-407, June.
    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. Christian Kanzow & Theresa Lechner, 2021. "Globalized inexact proximal Newton-type methods for nonconvex composite functions," Computational Optimization and Applications, Springer, vol. 78(2), pages 377-410, March.
    8. Yang Ann Shawing, 2015. "Measuring Self-Service Technology Latent Difficulties: Insurance Decisions on Utilitarian and Hedonic Influences," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 9(1), pages 1-33, January.
    9. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    10. Haibin Zhang & Juan Wei & Meixia Li & Jie Zhou & Miantao Chao, 2014. "On proximal gradient method for the convex problems regularized with the group reproducing kernel norm," Journal of Global Optimization, Springer, vol. 58(1), pages 169-188, January.
    11. Berriel, Tiago & Medeiros, Marcelo C. & Sena, Marcelo J., 2016. "Instrument selection for estimation of a forward-looking Phillips Curve," Economics Letters, Elsevier, vol. 145(C), pages 123-125.
    12. Saptarshi Chakraborty & Colin B. Begg & Ronglai Shen, 2021. "Using the “Hidden” genome to improve classification of cancer types," Biometrics, The International Biometric Society, vol. 77(4), pages 1445-1455, December.
    13. Qing Wang & Dan Zhao, 2019. "Penalization methods with group-wise sparsity: econometric applications to eBay Motors online auctions," Empirical Economics, Springer, vol. 57(2), pages 683-704, August.
    14. Karsten Schweikert, 2022. "Detecting Multiple Structural Breaks in Systems of Linear Regression Equations with Integrated and Stationary Regressors," Papers 2201.05430, arXiv.org, revised Sep 2024.
    15. Nibbering, Didier & Hastie, Trevor J., 2022. "Multiclass-penalized logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    16. Pilar Lopez-Llompart & G. Mathias Kondolf, 2016. "Encroachments in floodways of the Mississippi River and Tributaries Project," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(1), pages 513-542, March.
    17. Cheng, Jianquan & Bertolini, Luca, 2013. "Measuring urban job accessibility with distance decay, competition and diversity," Journal of Transport Geography, Elsevier, vol. 30(C), pages 100-109.
    18. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    19. Prilly Oktoviany & Robert Knobloch & Ralf Korn, 2021. "A machine learning-based price state prediction model for agricultural commodities using external factors," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1063-1085, December.
    20. Michelle Sheran Sylvester, 2007. "The Career and Family Choices of Women: A Dynamic Analysis of Labor Force Participation, Schooling, Marriage and Fertility Decisions," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(3), pages 367-399, July.

    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:coopap:v:61:y:2015:i:1:p:79-99. 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.