IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v104y2000i3d10.1023_a1004689609425.html
   My bibliography  Save this article

Efficiency of Proximal Bundle Methods

Author

Listed:
  • K. C. Kiwiel

    (Systems Research Institute)

Abstract

We give efficiency estimates for proximal bundle methods for finding f*≔minXf, where f and X are convex. We show that, for any accuracy ∈

Suggested Citation

  • K. C. Kiwiel, 2000. "Efficiency of Proximal Bundle Methods," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 589-603, March.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:3:d:10.1023_a:1004689609425
    DOI: 10.1023/A:1004689609425
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1004689609425
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1004689609425?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. Nesterov, Y., 1995. "Complexity estimates of some cutting plane methods based on the analytic barrier," LIDAM Reprints CORE 1167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 5-11, August.
    3. Krzysztof C. Kiwiel & Torbjörn Larsson & P. O. Lindberg, 1999. "The Efficiency of Ballstep Subgradient Level Methods for Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 237-254, February.
    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. Demyanov, Alexey V. & Fuduli, Antonio & Miglionico, Giovanna, 2007. "A bundle modification strategy for convex minimization," European Journal of Operational Research, Elsevier, vol. 180(1), pages 38-47, July.
    2. A. Fuduli & M. Gaudioso, 2006. "Tuning Strategy for the Proximity Parameter in Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 95-112, July.
    3. Krzysztof C. Kiwiel & Torbjörn Larsson & P. O. Lindberg, 2007. "Lagrangian Relaxation via Ballstep Subgradient Methods," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 669-686, August.
    4. Benjamin Grimmer, 2023. "General Hölder Smooth Convergence Rates Follow from Specialized Rates Assuming Growth Bounds," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 51-70, April.
    5. Tang, Chunming & Liu, Shuai & Jian, Jinbao & Ou, Xiaomei, 2020. "A multi-step doubly stabilized bundle method for nonsmooth convex optimization," Applied Mathematics and Computation, Elsevier, vol. 376(C).

    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. Júlíus Atlason & Marina A. Epelman & Shane G. Henderson, 2008. "Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods," Management Science, INFORMS, vol. 54(2), pages 295-309, February.
    2. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 2003. "On the convergence of conditional [var epsilon]-subgradient methods for convex programs and convex-concave saddle-point problems," European Journal of Operational Research, Elsevier, vol. 151(3), pages 461-473, December.
    3. Jie Shen & Ya-Li Gao & Fang-Fang Guo & Rui Zhao, 2018. "A Redistributed Bundle Algorithm for Generalized Variational Inequality Problems in Hilbert Spaces," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-18, August.
    4. Krzysztof C. Kiwiel & Torbjörn Larsson & P. O. Lindberg, 2007. "Lagrangian Relaxation via Ballstep Subgradient Methods," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 669-686, August.
    5. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
    6. Sitters, R.A., 2009. "Efficient algorithms for average completion time scheduling," Serie Research Memoranda 0058, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. J. R. Birge & L. Qi & Z. Wei, 1998. "Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 357-383, May.
    8. E. Y. Pee & J. O. Royset, 2011. "On Solving Large-Scale Finite Minimax Problems Using Exponential Smoothing," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 390-421, February.
    9. Y. R. He, 2001. "Minimizing and Stationary Sequences of Convex Constrained Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 137-153, October.
    10. Jinpeng Ma & Qiongling Li, 2016. "Convergence of price processes under two dynamic double auctions," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 1-44, December.
    11. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Other publications TiSEM 77da022b-635b-46fd-bf4a-f, Tilburg University, School of Economics and Management.
    12. Antonio Frangioni, 2005. "About Lagrangian Methods in Integer Optimization," Annals of Operations Research, Springer, vol. 139(1), pages 163-193, October.
    13. J.-P. Penot & P. H. Quang, 1997. "Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 343-356, February.
    14. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2022. "Essentials of numerical nonsmooth optimization," Annals of Operations Research, Springer, vol. 314(1), pages 213-253, July.
    15. Z. Wei & L. Qi & H. Jiang, 1997. "Some Convergence Properties of Descent Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 177-188, October.
    16. J. P. Penot & P. H. Sach, 1997. "Generalized Monotonicity of Subdifferentials and Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 251-262, July.
    17. R. Cominetti, 1997. "Coupling the Proximal Point Algorithm with Approximation Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 581-600, December.
    18. Joe Naoum-Sawaya & Samir Elhedhli, 2013. "An interior-point Benders based branch-and-cut algorithm for mixed integer programs," Annals of Operations Research, Springer, vol. 210(1), pages 33-55, November.
    19. A. I. Rauf & M. Fukushima, 2000. "Globally Convergent BFGS Method for Nonsmooth Convex Optimization1," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 539-558, March.
    20. Zhou, Bojian & Bliemer, Michiel & Yang, Hai & He, Jie, 2015. "A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 77-92.

    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:104:y:2000:i:3:d:10.1023_a:1004689609425. 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.