期刊
MATHEMATICAL PROGRAMMING
卷 100, 期 3, 页码 589-611出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-004-0507-x
关键词
probabilistic constraints; chance constraints; Lipschitz stability; stochastic optimization
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 Holder 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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