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A framework of distributionally robust possibilistic optimization

Author

Listed:
  • Romain Guillaume

    (Université de Toulouse-IRIT Toulouse)

  • Adam Kasperski

    (Wrocław University of Science and Technology)

  • Paweł Zieliński

    (Wrocław University of Science and Technology)

Abstract

In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called scenarios, is specified. This possibility distribution induces a necessity measure in a scenario set, which in turn describes an ambiguity set of probability distributions in a scenario set. The distributionally robust approach is then used to convert the imprecise constraints into deterministic equivalents. Namely, the left-hand side of an imprecise constraint is evaluated by using a risk measure with respect to the worst probability distribution that can occur. In this paper, the Conditional Value at Risk is used as the risk measure, which generalizes the strict robust, and expected value approaches commonly used in literature. A general framework for solving such a class of problems is described. Some cases which can be solved in polynomial time are identified.

Suggested Citation

  • Romain Guillaume & Adam Kasperski & Paweł Zieliński, 2024. "A framework of distributionally robust possibilistic optimization," Fuzzy Optimization and Decision Making, Springer, vol. 23(2), pages 253-278, June.
    • Handle: RePEc:spr:fuzodm:v:23:y:2024:i:2:d:10.1007_s10700-024-09420-2
    DOI: 10.1007/s10700-024-09420-2
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    References listed on IDEAS

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    1. Dubois, Didier, 2006. "Possibility theory and statistical reasoning," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 47-69, November.
    2. Baudrit, C. & Dubois, D., 2006. "Practical representations of incomplete probabilistic knowledge," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 86-108, November.
    3. de Klerk, Etienne & Laurent, Monique, 2019. "A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis," Other publications TiSEM d956492f-3e25-4dda-a5e2-e, Tilburg University, School of Economics and Management.
    4. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
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