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

Abstract

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|Ax ≥ z} , where A is a matrix of order (s, m) and the inequality sign has to be understood component-wise.