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Efficiency of Proximal Bundle Methods

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  • 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
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    References listed on IDEAS

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    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 1-7, 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.
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    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).

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