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

• 成果类型: Article
• 署名作者: Henrion, R; Römisch, W
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-004-0507-x
• 发表日期: 2004
• 页码: 589-611
• 关键词: quantitative stability; stochastic programs

摘要

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.