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Existence of solutions for a class of bilevel stochastic linear programs

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  • Claus, Matthias

Abstract

We study bilevel stochastic linear programs where the upper and lower level goal functions as well as the right-hand side of the follower’s constraint system are affected by randomness. Invoking a robust representation result, we prove that any objective functional derived from a convex risk measure is lower semicontinuous, even if the underlying distribution is not absolutely continuous with respect to the Lebesgue measure. Moreover, we provide a continuity result that also applies to pessimistic models and show that the existence of solutions can be guaranteed under standard compactness assumptions.

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  • Claus, Matthias, 2022. "Existence of solutions for a class of bilevel stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 299(2), pages 542-549.
    • Handle: RePEc:eee:ejores:v:299:y:2022:i:2:p:542-549
    DOI: 10.1016/j.ejor.2021.12.004
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    References listed on IDEAS

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