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Randomized Progressive Hedging methods for multi-stage stochastic programming

Author

Listed:
  • Gilles Bareilles

    (Univ. Grenoble Alpes)

  • Yassine Laguel

    (Univ. Grenoble Alpes)

  • Dmitry Grishchenko

    (Univ. Grenoble Alpes)

  • Franck Iutzeler

    (Univ. Grenoble Alpes)

  • Jérôme Malick

    (CNRS and LJK)

Abstract

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this paper, we introduce randomized versions of the Progressive Hedging algorithm able to produce new iterates as soon as a single scenario subproblem is solved. Building on the relation between Progressive Hedging and monotone operators, we leverage recent results on randomized fixed point methods to derive and analyze the proposed methods. Finally, we release the corresponding code as an easy-to-use Julia toolbox and report computational experiments showing the practical interest of randomized algorithms, notably in a parallel context. Throughout the paper, we pay a special attention to presentation, stressing main ideas, avoiding extra-technicalities, in order to make the randomized methods accessible to a broad audience in the Operations Research community.

Suggested Citation

  • Gilles Bareilles & Yassine Laguel & Dmitry Grishchenko & Franck Iutzeler & Jérôme Malick, 2020. "Randomized Progressive Hedging methods for multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 295(2), pages 535-560, December.
    • Handle: RePEc:spr:annopr:v:295:y:2020:i:2:d:10.1007_s10479-020-03811-5
    DOI: 10.1007/s10479-020-03811-5
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    References listed on IDEAS

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    1. Jonathan Eckstein, 2017. "A Simplified Form of Block-Iterative Operator Splitting and an Asynchronous Algorithm Resembling the Multi-Block Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 155-182, April.
    2. Jean-Paul Watson & David Woodruff, 2011. "Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems," Computational Management Science, Springer, vol. 8(4), pages 355-370, November.
    3. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    4. R. Tyrrell Rockafellar & Johannes O. Royset, 2018. "Superquantile/CVaR risk measures: second-order theory," Annals of Operations Research, Springer, vol. 262(1), pages 3-28, March.
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