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Progressive hedging for stochastic programs with cross-scenario inequality constraints

Author

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  • Ellen Krohn Aasgård

    (Norwegian University of Science and Technology)

  • Hans Ivar Skjelbred

    (SINTEF Energy Research)

Abstract

In this paper, we show how progressive hedging may be used to solve stochastic programming problems that involve cross-scenario inequality constraints. In contrast, standard stochastic programs involve cross-scenario equality constraints that describe the non-anticipative nature of the optimal solution. The standard progressive hedging algorithm (PHA) iteratively manipulates the objective function coefficients of the scenario subproblems to reflect the costs of non-anticipativity and penalize deviations from a non-anticipative, aggregated solution. Our proposed algorithm follows the same principle, but works with cross-scenario inequality constraints. Specifically, we focus on the problem of determining optimal bids for hydropower producers that participate in wholesale electricity auctions. The cross-scenario inequality constraints arise from the fact that bids are required to be non-decreasing. We show that PHA for inequality constraints have the same convergence properties as standard PHA, and illustrate our algorithm with results for an instance of the hydropower bidding problem.

Suggested Citation

  • Ellen Krohn Aasgård & Hans Ivar Skjelbred, 2020. "Progressive hedging for stochastic programs with cross-scenario inequality constraints," Computational Management Science, Springer, vol. 17(1), pages 141-160, January.
    • Handle: RePEc:spr:comgts:v:17:y:2020:i:1:d:10.1007_s10287-019-00359-z
    DOI: 10.1007/s10287-019-00359-z
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    References listed on IDEAS

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    1. Séguin, Sara & Fleten, Stein-Erik & Côté, Pascal & Pichler, Alois & Audet, Charles, 2017. "Stochastic short-term hydropower planning with inflow scenario trees," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1156-1168.
    2. 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.
    3. 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.
    4. Fleten, Stein-Erik & Kristoffersen, Trine Krogh, 2007. "Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer," European Journal of Operational Research, Elsevier, vol. 181(2), pages 916-928, September.
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