IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v176y2018i3d10.1007_s10957-018-1226-4.html
   My bibliography  Save this article

On the Proximal Gradient Algorithm with Alternated Inertia

Author

Listed:
  • Franck Iutzeler

    (University of Grenoble Alpes)

  • Jérôme Malick

    (CNRS, LJK)

Abstract

In this paper, we investigate attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm with alternated inertia, based on local geometric properties of the objective function. The results are put into perspective by discussions on several extensions (strongly convex case, non-convex case, and alternated extrapolation) and illustrations on common regularized optimization problems.

Suggested Citation

  • Franck Iutzeler & Jérôme Malick, 2018. "On the Proximal Gradient Algorithm with Alternated Inertia," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 688-710, March.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:3:d:10.1007_s10957-018-1226-4
    DOI: 10.1007/s10957-018-1226-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1226-4
    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/s10957-018-1226-4?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. Marc Fuentes & Jérôme Malick & Claude Lemaréchal, 2012. "Descentwise inexact proximal algorithms for smooth optimization," Computational Optimization and Applications, Springer, vol. 53(3), pages 755-769, December.
    2. Pierre Frankel & Guillaume Garrigos & Juan Peypouquet, 2015. "Splitting Methods with Variable Metric for Kurdyka–Łojasiewicz Functions and General Convergence Rates," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 874-900, June.
    3. A. Chambolle & Ch. Dossal, 2015. "On the Convergence of the Iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm”," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 968-982, September.
    4. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Yekini Shehu & Qiao-Li Dong & Lulu Liu & Jen-Chih Yao, 2023. "Alternated inertial subgradient extragradient method for equilibrium problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-30, April.
    2. Ferdinard U. Ogbuisi & Yekini Shehu & Jen-Chih Yao, 2023. "Relaxed Single Projection Methods for Solving Bilevel Variational Inequality Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(3), pages 641-678, September.
    3. Seakweng Vong & Zhongsheng Yao, 2024. "Modified general splitting method for the split feasibility problem," Journal of Global Optimization, Springer, vol. 90(3), pages 711-726, November.
    4. Luis M. Briceño-Arias & Giovanni Chierchia & Emilie Chouzenoux & Jean-Christophe Pesquet, 2019. "A random block-coordinate Douglas–Rachford splitting method with low computational complexity for binary logistic regression," Computational Optimization and Applications, Springer, vol. 72(3), pages 707-726, April.
    5. Wenli Huang & Yuchao Tang & Meng Wen & Haiyang Li, 2022. "Relaxed Variable Metric Primal-Dual Fixed-Point Algorithm with Applications," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    6. Huan Zhang & Xiaolan Liu & Yan Sun & Ju Hu, 2023. "An Alternated Inertial Projection Algorithm for Multi-Valued Variational Inequality and Fixed Point Problems," Mathematics, MDPI, vol. 11(8), pages 1-13, April.
    7. Gilles Bareilles & Franck Iutzeler, 2020. "On the interplay between acceleration and identification for the proximal gradient algorithm," Computational Optimization and Applications, Springer, vol. 77(2), pages 351-378, 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. 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.
    2. Szilárd Csaba László, 2023. "A Forward–Backward Algorithm With Different Inertial Terms for Structured Non-Convex Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 387-427, July.
    3. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    4. Masaru Ito, 2016. "New results on subgradient methods for strongly convex optimization problems with a unified analysis," Computational Optimization and Applications, Springer, vol. 65(1), pages 127-172, September.
    5. TAYLOR, Adrien B. & HENDRICKX, Julien M. & François GLINEUR, 2016. "Exact worst-case performance of first-order methods for composite convex optimization," LIDAM Discussion Papers CORE 2016052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Dimitris Bertsimas & Nishanth Mundru, 2021. "Sparse Convex Regression," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 262-279, January.
    7. Lazzaro, D. & Loli Piccolomini, E. & Zama, F., 2019. "A fast splitting method for efficient Split Bregman iterations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 139-146.
    8. Glaydston Carvalho Bento & João Xavier Cruz Neto & Antoine Soubeyran & Valdinês Leite Sousa Júnior, 2016. "Dual Descent Methods as Tension Reduction Systems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 209-227, October.
    9. Alexandre Belloni & Victor Chernozhukov & Lie Wang, 2013. "Pivotal estimation via square-root lasso in nonparametric regression," CeMMAP working papers CWP62/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2013. "First-order methods with inexact oracle: the strongly convex case," LIDAM Discussion Papers CORE 2013016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
    12. David Degras, 2021. "Sparse group fused lasso for model segmentation: a hybrid approach," 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. 15(3), pages 625-671, September.
    13. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.
    14. Yunmei Chen & Xiaojing Ye & Wei Zhang, 2020. "Acceleration techniques for level bundle methods in weakly smooth convex constrained optimization," Computational Optimization and Applications, Springer, vol. 77(2), pages 411-432, November.
    15. 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.
    16. Wenjie Huang & Xun Zhang, 2021. "Randomized Smoothing Variance Reduction Method for Large-Scale Non-smooth Convex Optimization," SN Operations Research Forum, Springer, vol. 2(2), pages 1-28, June.
    17. Le Thi Khanh Hien & Cuong V. Nguyen & Huan Xu & Canyi Lu & Jiashi Feng, 2019. "Accelerated Randomized Mirror Descent Algorithms for Composite Non-strongly Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 541-566, May.
    18. DEVOLDER, Olivier, 2011. "Stochastic first order methods in smooth convex optimization," LIDAM Discussion Papers CORE 2011070, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Boriss Siliverstovs, 2017. "Short-term forecasting with mixed-frequency data: a MIDASSO approach," Applied Economics, Taylor & Francis Journals, vol. 49(13), pages 1326-1343, March.
    20. Ya-Feng Liu & Xin Liu & Shiqian Ma, 2019. "On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 632-650, 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:joptap:v:176:y:2018:i:3:d:10.1007_s10957-018-1226-4. 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.