IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v64y2016i1d10.1007_s10589-015-9802-0.html
   My bibliography  Save this article

An adaptive accelerated first-order method for convex optimization

Author

Listed:
  • Renato D. C. Monteiro

    (Georgia Institute of Technology)

  • Camilo Ortiz

    (Georgia Institute of Technology)

  • Benar F. Svaiter

    (IMPA)

Abstract

This paper presents a new accelerated variant of Nesterov’s method for solving composite convex optimization problems in which certain acceleration parameters are adaptively (and aggressively) chosen so as to substantially improve its practical performance compared to existing accelerated variants while at the same time preserve the optimal iteration-complexity shared by these methods. Computational results are presented to demonstrate that the proposed adaptive accelerated method endowed with a restarting scheme outperforms other existing accelerated variants.

Suggested Citation

  • Renato D. C. Monteiro & Camilo Ortiz & Benar F. Svaiter, 2016. "An adaptive accelerated first-order method for convex optimization," Computational Optimization and Applications, Springer, vol. 64(1), pages 31-73, May.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9802-0
    DOI: 10.1007/s10589-015-9802-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-015-9802-0
    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/s10589-015-9802-0?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. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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).
    3. M. Merritt & Y. Zhang, 2005. "Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 191-202, July.
    4. NESTEROV, Yu., 2007. "Gradient methods for minimizing composite objective function," LIDAM Discussion Papers CORE 2007076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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. Donghwan Kim & Jeffrey A. Fessler, 2018. "Adaptive Restart of the Optimized Gradient Method for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 240-263, July.
    2. Maicon Marques Alves & Samara Costa Lima, 2017. "An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 818-847, December.
    3. Weiwei Kong & Renato D. C. Monteiro, 2023. "An accelerated inexact dampened augmented Lagrangian method for linearly-constrained nonconvex composite optimization problems," Computational Optimization and Applications, Springer, vol. 85(2), pages 509-545, June.
    4. Weiwei Kong & Jefferson G. Melo & Renato D. C. Monteiro, 2020. "An efficient adaptive accelerated inexact proximal point method for solving linearly constrained nonconvex composite problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 305-346, June.
    5. Weiwei Kong & Renato D. C. Monteiro, 2022. "Accelerated inexact composite gradient methods for nonconvex spectral optimization problems," Computational Optimization and Applications, Springer, vol. 82(3), pages 673-715, July.
    6. 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.

    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. Jueyou Li & Zhiyou Wu & Changzhi Wu & Qiang Long & Xiangyu Wang, 2016. "An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 153-171, January.
    2. 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.
    3. 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).
    4. Masoud Ahookhosh, 2019. "Accelerated first-order methods for large-scale convex optimization: nearly optimal complexity under strong convexity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 319-353, June.
    5. 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).
    6. Lingxue Zhang & Seyoung Kim, 2014. "Learning Gene Networks under SNP Perturbations Using eQTL Datasets," PLOS Computational Biology, Public Library of Science, vol. 10(2), pages 1-20, February.
    7. 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.
    8. 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.
    9. 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).
    10. 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.
    11. Majid Jahani & Naga Venkata C. Gudapati & Chenxin Ma & Rachael Tappenden & Martin Takáč, 2021. "Fast and safe: accelerated gradient methods with optimality certificates and underestimate sequences," Computational Optimization and Applications, Springer, vol. 79(2), pages 369-404, June.
    12. Stefan Richter & Colin Jones & Manfred Morari, 2013. "Certification aspects of the fast gradient method for solving the dual of parametric convex programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 305-321, June.
    13. J. O. Royset & E. Y. Pee, 2012. "Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 855-882, December.
    14. Qihang Lin & Xi Chen & Javier Peña, 2014. "A sparsity preserving stochastic gradient methods for sparse regression," Computational Optimization and Applications, Springer, vol. 58(2), pages 455-482, June.
    15. Xiubo Liang & Guoqiang Wang & Bo Yu, 2022. "A reduced proximal-point homotopy method for large-scale non-convex BQP," Computational Optimization and Applications, Springer, vol. 81(2), pages 539-567, March.
    16. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2013. "Intermediate gradient methods for smooth convex problems with inexact oracle," LIDAM Discussion Papers CORE 2013017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Lorenzo Rosasco & Silvia Villa & Bang Công Vũ, 2016. "Stochastic Forward–Backward Splitting for Monotone Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 388-406, May.
    18. Masoud Ahookhosh & Arnold Neumaier, 2018. "Solving structured nonsmooth convex optimization with complexity $$\mathcal {O}(\varepsilon ^{-1/2})$$ O ( ε - 1 / 2 )," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 110-145, April.
    19. Bo Wen & Xiaoping Xue, 2019. "On the convergence of the iterates of proximal gradient algorithm with extrapolation for convex nonsmooth minimization problems," Journal of Global Optimization, Springer, vol. 75(3), pages 767-787, November.
    20. Guoqiang Wang & Bo Yu, 2019. "PAL-Hom method for QP and an application to LP," Computational Optimization and Applications, Springer, vol. 73(1), pages 311-352, May.

    More about this item

    Statistics

    Access and download statistics

    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:64:y:2016:i:1:d:10.1007_s10589-015-9802-0. 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.