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SPEPS Preprint

Author(s): René Henrion, Weierstrass Institute
Werner Römisch, Humboldt-Unversity Berlin
Title: Hölder and Lipschitz Stability of Solution Sets in Programs with Probabilistic Constraints
Date of Acceptance: 06.03.2003
Submission Date: 13.12.2003
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): probabilistic constraints, chance constraints, stochastic optimization, Lipschitz stability
Appeared in: Mathematical programming 3 (Vol. 100, 2004)
Springer (Berlin [u.a.])
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Abstract (eng):
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 an 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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