IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v91y2025i3d10.1007_s10898-024-01441-w.html
   My bibliography  Save this article

Iterative mix thresholding algorithm with continuation technique for mix sparse optimization and application

Author

Listed:
  • Yaohua Hu

    (Shenzhen University)

  • Jian Lu

    (Shenzhen University)

  • Xiaoqi Yang

    (The Hong Kong Polytechnic University, Kowloon)

  • Kai Zhang

    (Shenzhen University
    Guangdong University of Finance and Economics)

Abstract

Mix sparse structure is inherited in a wide class of practical applications, namely, the sparse structure appears as the inter-group and intra-group manners simultaneously. In this paper, we propose an iterative mix thresholding algorithm with continuation technique (IMTC) to solve the $$\ell _0$$ ℓ 0 regularized mix sparse optimization. The significant advantage of the IMTC is that it has a closed-form expression and low storage requirement, and it is able to promote the mix sparse structure of the solution. We prove the convergence property and the linear convergence rate of the ITMC to a local minimum; moreover, we show that the ITMC approaches an approximate true mix sparse solution within a tolerance relevant to the noise level under an assumption of restricted isometry property. We also apply the mix sparse optimization to model the differential optical absorption spectroscopy analysis with the wavelength misalignment, and numerical results indicate that the IMTC can exactly and quantitatively predict the existing materials and the factual wavelength misalignment simultaneously within 0.1 s, which meets the demand of improvement of the automatic analysis software.

Suggested Citation

  • Yaohua Hu & Jian Lu & Xiaoqi Yang & Kai Zhang, 2025. "Iterative mix thresholding algorithm with continuation technique for mix sparse optimization and application," Journal of Global Optimization, Springer, vol. 91(3), pages 511-534, March.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:3:d:10.1007_s10898-024-01441-w
    DOI: 10.1007/s10898-024-01441-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-024-01441-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/s10898-024-01441-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. 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. Yanming Li & Bin Nan & Ji Zhu, 2015. "Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure," Biometrics, The International Biometric Society, vol. 71(2), pages 354-363, June.
    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. Yaohua Hu & Chong Li & Kaiwen Meng & Xiaoqi Yang, 2021. "Linear convergence of inexact descent method and inexact proximal gradient algorithms for lower-order regularization problems," Journal of Global Optimization, Springer, vol. 79(4), pages 853-883, April.
    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. Chen, Yang & Luo, Ziyan & Kong, Lingchen, 2021. "ℓ2,0-norm based selection and estimation for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. 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.
    3. Wentao Wang & Jiaxuan Liang & Rong Liu & Yunquan Song & Min Zhang, 2022. "A Robust Variable Selection Method for Sparse Online Regression via the Elastic Net Penalty," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    4. Srinivasan, Arun & Xue, Lingzhou & Zhan, Xiang, 2023. "Identification of microbial features in multivariate regression under false discovery rate control," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    5. Yu-Zhu Tian & Man-Lai Tang & Mao-Zai Tian, 2021. "Bayesian joint inference for multivariate quantile regression model with L $$_{1/2}$$ 1 / 2 penalty," Computational Statistics, Springer, vol. 36(4), pages 2967-2994, December.
    6. 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.
    7. 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).
    8. 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.
    9. Singh, Rakhi & Stufken, John, 2024. "Factor selection in screening experiments by aggregation over random models," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    10. Koki Momoki & Takuma Yoshida, 2024. "Hypothesis testing for varying coefficient models in tail index regression," Statistical Papers, Springer, vol. 65(6), pages 3821-3852, August.
    11. 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.
    12. 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.
    13. 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.
    14. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    15. Hang Yu & Yuanjia Wang & Donglin Zeng, 2023. "A general framework of nonparametric feature selection in high‐dimensional data," Biometrics, The International Biometric Society, vol. 79(2), pages 951-963, June.
    16. Qianyun Li & Runmin Shi & Faming Liang, 2019. "Drug sensitivity prediction with high-dimensional mixture regression," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-18, February.
    17. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    18. Gerda Claeskens & Maarten Jansen, 2023. "Comments on: Statistical inference and large-scale multiple testing for high-dimensional regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1177-1179, December.
    19. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    20. Zak-Szatkowska, Malgorzata & Bogdan, Malgorzata, 2011. "Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2908-2924, November.

    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:91:y:2025:i:3:d:10.1007_s10898-024-01441-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.