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An ADMM algorithm for two-stage stochastic programming problems

  • S.I.: CLAIO 2016
  • Published:
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Abstract

The alternate direction method of multipliers (ADMM) has received significant attention recently as a powerful algorithm to solve convex problems with a block structure. The vast majority of applications focus on deterministic problems. In this paper we show that ADMM can be applied to solve two-stage stochastic programming problems, and we propose an implementation in three blocks with or without proximal terms. We present numerical results for large scale instances, and extend our findings for risk averse formulations using utility functions.

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Notes

  1. Note that in this case it would be more appropriate to call it a “disutility function” in line with the literature, but we keep our terminology for simplicity.

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Acknowledgements

The authors thank two anonymous referees for their constructive comments, which in particular allowed us to provide a generic formulation of the algorithm that includes the cases with and without proximal terms. This research was supported by FONDECYT Project No. 1171145.

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Authors and Affiliations

  1. School of Business, Universidad Adolfo Ibáñez, Santiago, Chile

    Sebastián Arpón, Tito Homem-de-Mello & Bernardo K. Pagnoncelli

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  1. Sebastián Arpón
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  2. Tito Homem-de-Mello
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  3. Bernardo K. Pagnoncelli
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Correspondence to Tito Homem-de-Mello.

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Arpón, S., Homem-de-Mello, T. & Pagnoncelli, B.K. An ADMM algorithm for two-stage stochastic programming problems. Ann Oper Res 286, 559–582 (2020). https://doi.org/10.1007/s10479-019-03471-0

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