R. Henrion et W. Romisch, Metric regularity and quantitative stability in stochastic programs with probabilistic constraints, MATH PROGR, 84(1), 1999, pp. 55-88
Introducing probabilistic constraints leads in general to nonconvex, nonsmo
oth or even discontinuous optimization models. In this paper, necessary and
sufficient conditions for metric regularity of(several joint) probabilisti
c constraints are derived using recent results from nonsmooth analysis. The
conditions apply to fairly general constraints and extend earlier work in
this direction. Further. a verifiable sufficient condition for quadratic gr
owth of the objective function in a more specific convex stochastic program
is indicated and applied in order to obtain a new result on quantitative s
tability of solution sets when the underlying probability distribution is s
ubjected to perturbations. This is used to derive bounds for the deviation
of solution sets when the probability measure is replaced by empirical esti
mates.