|edoc-Server der Humboldt-Universität zu Berlin|
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|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Keywords (eng):||probabilistic constraints, chance constraints, stochastic optimization, Lipschitz stability|
Mathematical programming 3 (Vol. 100, 2004)
Springer (Berlin [u.a.])
|Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link.||Endnote Bibtex|
|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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