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Uncontrolled inexact information within bundle methods

Author

Listed:
  • Jérôme Malick

    (CNRS, LJK)

  • Welington Oliveira

    (UERJ
    BCAM)

  • Sofia Zaourar

    (INRIA, UJF
    Xerox Research Centre Europe)

Abstract

We consider convex non-smooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition. In this paper, we study how to incorporate the uncontrolled linearizations into (proximal and level) bundle algorithms in view of generating better iterates and possibly accelerating the methods. We provide the convergence analysis of the algorithms using uncontrolled linearizations, and we present numerical illustrations showing they indeed speed up resolution of two stochastic optimization problems coming from energy optimization (two-stage linear problems and chance-constrained problems in reservoir management).

Suggested Citation

  • Jérôme Malick & Welington Oliveira & Sofia Zaourar, 2017. "Uncontrolled inexact information within bundle methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 5-29, March.
    • Handle: RePEc:spr:eurjco:v:5:y:2017:i:1:d:10.1007_s13675-015-0060-9
    DOI: 10.1007/s13675-015-0060-9
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    References listed on IDEAS

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    1. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    2. Gerd Infanger (ed.), 2011. "Stochastic Programming," International Series in Operations Research and Management Science, Springer, number 978-1-4419-1642-6, September.
    3. M. V. Solodov, 2003. "On Approximations with Finite Precision in Bundle Methods for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 151-165, October.
    4. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
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    Cited by:

    1. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Adaptive Bundle Methods for Nonlinear Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2106-2124, July.
    2. Wim Ackooij & Nicolas Lebbe & Jérôme Malick, 2017. "Regularized decomposition of large scale block-structured robust optimization problems," Computational Management Science, Springer, vol. 14(3), pages 393-421, July.

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