IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v82y2022i1d10.1007_s10589-022-00357-z.html
   My bibliography  Save this article

An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems

Author

Listed:
  • Tianxiang Liu

    (Tokyo Institute of Technology)

  • Akiko Takeda

    (The University of Tokyo
    Center for Advanced Intelligence Project)

Abstract

In this paper, we propose a new method for a class of difference-of-convex (DC) optimization problems, whose objective is the sum of a smooth function and a possibly non-prox-friendly DC function. The method sequentially solves subproblems constructed from a quadratic approximation of the smooth function and a linear majorization of the concave part of the DC function. We allow the subproblem to be solved inexactly, and propose a new inexact rule to characterize the inexactness of the approximate solution. For several classical algorithms applied to the subproblem, we derive practical termination criteria so as to obtain solutions satisfying the inexact rule. We also present some convergence results for our method, including the global subsequential convergence and a non-asymptotic complexity analysis. Finally, numerical experiments are conducted to illustrate the efficiency of our method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00357-z
    DOI: 10.1007/s10589-022-00357-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-022-00357-z
    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/s10589-022-00357-z?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. Emilie Chouzenoux & Jean-Christophe Pesquet & Audrey Repetti, 2014. "Variable Metric Forward–Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 107-132, July.
    2. Jinchao Li & Martin S. Andersen & Lieven Vandenberghe, 2017. "Inexact proximal Newton methods for self-concordant functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 19-41, February.
    3. 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.
    4. Hiva Ghanbari & Katya Scheinberg, 2018. "Proximal quasi-Newton methods for regularized convex optimization with linear and accelerated sublinear convergence rates," Computational Optimization and Applications, Springer, vol. 69(3), pages 597-627, April.
    5. Lorenzo Stella & Andreas Themelis & Panagiotis Patrinos, 2017. "Forward–backward quasi-Newton methods for nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 443-487, July.
    6. Shummin Nakayama & Yasushi Narushima & Hiroshi Yabe, 2021. "Inexact proximal memoryless quasi-Newton methods based on the Broyden family for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 79(1), pages 127-154, May.
    7. 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.
    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. Wei Peng & Hui Zhang & Xiaoya Zhang & Lizhi Cheng, 2020. "Global complexity analysis of inexact successive quadratic approximation methods for regularized optimization under mild assumptions," Journal of Global Optimization, Springer, vol. 78(1), pages 69-89, September.
    10. 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.
    11. Ching-pei Lee & Stephen J. Wright, 2019. "Inexact Successive quadratic approximation for regularized optimization," Computational Optimization and Applications, Springer, vol. 72(3), pages 641-674, 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. 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.
    2. Ching-pei Lee & Stephen J. Wright, 2019. "Inexact Successive quadratic approximation for regularized optimization," Computational Optimization and Applications, Springer, vol. 72(3), pages 641-674, April.
    3. 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.
    4. Bonettini, S. & Prato, M. & Rebegoldi, S., 2021. "New convergence results for the inexact variable metric forward–backward method," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Ching-pei Lee & Stephen J. Wright, 2020. "Inexact Variable Metric Stochastic Block-Coordinate Descent for Regularized Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 151-187, April.
    6. Silvia Bonettini & Peter Ochs & Marco Prato & Simone Rebegoldi, 2023. "An abstract convergence framework with application to inertial inexact forward–backward methods," Computational Optimization and Applications, Springer, vol. 84(2), pages 319-362, March.
    7. Peter Ochs, 2018. "Local Convergence of the Heavy-Ball Method and iPiano for Non-convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 153-180, April.
    8. S. Bonettini & M. Prato & S. Rebegoldi, 2018. "A block coordinate variable metric linesearch based proximal gradient method," Computational Optimization and Applications, Springer, vol. 71(1), pages 5-52, September.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Hongbo Dong & Min Tao, 2021. "On the Linear Convergence to Weak/Standard d-Stationary Points of DCA-Based Algorithms for Structured Nonsmooth DC Programming," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 190-220, April.
    14. 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.
    15. 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.
    16. 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.
    17. Shummin Nakayama & Yasushi Narushima & Hiroshi Yabe, 2021. "Inexact proximal memoryless quasi-Newton methods based on the Broyden family for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 79(1), pages 127-154, May.
    18. 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.
    19. Wei Peng & Hui Zhang & Xiaoya Zhang & Lizhi Cheng, 2020. "Global complexity analysis of inexact successive quadratic approximation methods for regularized optimization under mild assumptions," Journal of Global Optimization, Springer, vol. 78(1), pages 69-89, September.
    20. Daoli Zhu & Sien Deng & Minghua Li & Lei Zhao, 2021. "Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 889-918, 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:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00357-z. 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.