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A Second-Order Sufficient Optimality Condition for Risk-Neutral Bi-level Stochastic Linear Programs

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  • Matthias Claus

    (University Duisburg-Essen)

Abstract

The expectation functionals, which arise in risk-neutral bi-level stochastic linear models with random lower-level right-hand side, are known to be continuously differentiable, if the underlying probability measure has a Lebesgue density. We show that the gradient may fail to be local Lipschitz continuous under this assumption. Our main result provides sufficient conditions for Lipschitz continuity of the gradient of the expectation functional and paves the way for a second-order optimality condition in terms of generalized Hessians. Moreover, we study geometric properties of regions of strong stability and derive representation results, which may facilitate the computation of gradients.

Suggested Citation

  • Matthias Claus, 2021. "A Second-Order Sufficient Optimality Condition for Risk-Neutral Bi-level Stochastic Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 243-259, January.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:1:d:10.1007_s10957-020-01775-x
    DOI: 10.1007/s10957-020-01775-x
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    Cited by:

    1. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.

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