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A semi-infinite programming approach to two-stage stochastic linear programs with high-order moment constraints

Optimization Letters volume 12, pages 1237–1247 (2018)Cite this article

Abstract

We consider distributionally robust two-stage stochastic linear optimization problems with higher-order (say \(p\ge 3\) and even possibly irrational) moment constraints in their ambiguity sets. We suggest to solve the dual form of the problem by a semi-infinite programming approach, which deals with a much simpler reformulation than the conic optimization approach. Some preliminary numerical results are reported.

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Notes

  1. The set \(\Pi \) here is a simplified version of the set \(\Pi \) in Corollary 1.

  2. This is a slightly different version of Example 7.3 in the book of [5]. It is also the same production planning example in [1].

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Acknowledgements

The authors are in debt to five anonymous referees for their comments that help greatly in improving an earlier version of the manuscript. The research is partially supported by the Provost Chair Fund at National University of Singapore and by the Australian Research Council Grant DP160102819.

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Authors and Affiliations

  1. Department of Decision Sciences, National University of Singapore, Singapore, Singapore

    Sarah Yini Gao

  2. School of Science, Curtin University, Perth, Australia

    Jie Sun

  3. School of Business, National Universityof Singapore, Singapore, Singapore

    Jie Sun

  4. Department of Mathematics, National Cheng Kung University, Tainan, Taiwan

    Soon-Yi Wu

Authors
  1. Sarah Yini Gao
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  2. Jie Sun
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  3. Soon-Yi Wu
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Correspondence to Jie Sun.

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Gao, S.Y., Sun, J. & Wu, SY. A semi-infinite programming approach to two-stage stochastic linear programs with high-order moment constraints. Optim Lett 12, 1237–1247 (2018). https://doi.org/10.1007/s11590-016-1095-4

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  • DOI: https://doi.org/10.1007/s11590-016-1095-4

Keywords

  • Semi-infinite optimization
  • Stochastic programming