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Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints

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Abstract.

We study perturbations of a stochastic program with a probabilistic constraint and r-concave original probability distribution. First we improve our earlier results substantially and provide conditions implying Hölder continuity properties of the solution sets w.r.t. the Kolmogorov distance of probability distributions. Secondly, we derive an upper Lipschitz continuity property for solution sets under more restrictive conditions on the original program and on the perturbed probability measures. The latter analysis applies to linear-quadratic models and is based on work by Bonnans and Shapiro. The stability results are illustrated by numerical tests showing the different asymptotic behaviour of parametric and nonparametric estimates in a program with a normal probabilistic constraint.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, 10117, Berlin, Germany

    René Henrion

  2. Humboldt-University Berlin, Institute of Mathematics, 10099, Berlin, Germany

    Werner Römisch

Authors
  1. René Henrion
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  2. Werner Römisch
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Correspondence to René Henrion.

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Mathematics Subject Classification (2000): 90C15, 90C31

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Henrion, R., Römisch, W. Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints. Math. Program., Ser. A 100, 589–611 (2004). https://doi.org/10.1007/s10107-004-0507-x

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  • DOI: https://doi.org/10.1007/s10107-004-0507-x

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