Progressive hedging for stochastic programs with cross-scenario inequality constraints

Ellen Krohn Aasgård () and Hans Ivar Skjelbred
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Ellen Krohn Aasgård: Norwegian University of Science and Technology
Hans Ivar Skjelbred: SINTEF Energy Research

Computational Management Science, 2020, vol. 17, issue 1, No 8, 160 pages

Abstract: 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.

Keywords: Progressive hedging; Stochastic programming; Hydropower; Unit commitment; Electricity auctions (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10287-019-00359-z

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