Perturbation Analysis of Chance-constrained Programs under Variation of all Constraint Data

  • René Henrion
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 532)


A fairly general shape of chance constraint programs is
$$ (P) \min \{ g(x)|x \in X, \mu (H(x)) \ge p\} $$
where g: ℝ m → ℝ is a continuous objective function, \( X \subseteq \mathbb{R}^m \) is a closed subset of deterministic constraints, and the inequality defines a probabilistic constraint with H : ℝ m ⇉ ℝ s being a multifunction with closed graph, µ is a probability measure on s and p ∈ (0, 1) is some probability level. In the simplest case of linear chance constraints, g is linear, X is a polyhedron and H(x) = {z ∈ ℝ s |Axz} , where A is a matrix of order (s, m) and the inequality sign has to be understood component-wise.


Probability Measure Lower Semicontinuity Stochastic Program Perturbation Analysis Constraint Qualification 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • René Henrion
    • 1
  1. 1.Weierstrass InstituteBerlinGermany

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