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Level bundle methods for constrained convex optimization with various oracles


  • Wim Ackooij


  • Welington Oliveira



We propose restricted memory level bundle methods for minimizing constrained convex nonsmooth optimization problems whose objective and constraint functions are known through oracles (black-boxes) that might provide inexact information. Our approach is general and covers many instances of inexact oracles, such as upper, lower and on-demand accuracy oracles. We show that the proposed level bundle methods are convergent as long as the memory is restricted to at least four well chosen linearizations: two linearizations for the objective function, and two linearizations for the constraints. The proposed methods are particularly suitable for both joint chance-constrained problems and two-stage stochastic programs with risk measure constraints. The approach is assessed on realistic joint constrained energy problems, arising when dealing with robust cascaded-reservoir management. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
  • Handle: RePEc:spr:coopap:v:57:y:2014:i:3:p:555-597
    DOI: 10.1007/s10589-013-9610-3

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    References listed on IDEAS

    1. repec:spr:isorms:978-1-4419-1642-6 is not listed on IDEAS
    2. repec:spr:compst:v:71:y:2010:i:3:p:535-549 is not listed on IDEAS
    3. Dentcheva, Darinka & Martinez, Gabriela, 2012. "Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse," European Journal of Operational Research, Elsevier, vol. 219(1), pages 1-8.
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    Cited by:

    1. W. Ackooij & A. Frangioni & W. Oliveira, 2016. "Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support," Computational Optimization and Applications, Springer, vol. 65(3), pages 637-669, December.
    2. X. J. Tong & H. Xu & F. F. Wu & Z. Zhao, 2016. "Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system," Computational Management Science, Springer, vol. 13(3), pages 393-422, July.
    3. Wim Ackooij, 2017. "A comparison of four approaches from stochastic programming for large-scale unit-commitment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 119-147, March.
    4. repec:spr:comgts:v:14:y:2017:i:3:d:10.1007_s10287-017-0281-x is not listed on IDEAS
    5. 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.
    6. Welington Oliveira, 2016. "Regularized optimization methods for convex MINLP problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 665-692, October.
    7. Wim Ackooij, 2014. "Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 227-253, December.
    8. Wolf, Christian & Fábián, Csaba I. & Koberstein, Achim & Suhl, Leena, 2014. "Applying oracles of on-demand accuracy in two-stage stochastic programming – A computational study," European Journal of Operational Research, Elsevier, vol. 239(2), pages 437-448.


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