hal-02013571
https://ifp.hal.science/hal-02013571
doi:10.1007/s11228-017-0454-3
[IFP] IFP Energies Nouvelles
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[EDF] EDF
(Sub-)Differentiability of Probability Functions with Elliptical Distributions
van Ackooij, Wim
Aleksovska, I.
Munoz-Zuniga, M.
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
ART
Stochastic optimisation
Probabilistic constraints
Chance constraints
Gradients of probability functions
In this paper we investigate probability functions acting on nonlinear systems wherein the random vector can follow an elliptically symmetric distribution. We provide first and second order differentiability results as well as readily implementable formulæ. We also demonstrate that these formulæ can be readily employed within standard non-linear programming software through a set of illustrative numerical experiments.
2018-12
en
Set-Valued and Variational Analysis
Springer