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Set-Valued and Variational Analysis

, Volume 26, Issue 4, pp 887–910 | Cite as

(Sub-)Differentiability of Probability Functions with Elliptical Distributions

  • W. van AckooijEmail author
  • I. Aleksovska
  • M. Munoz-Zuniga
Article

Abstract

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.

Keywords

Stochastic optimisation Probabilistic constraints Chance constraints Gradients of probability functions 

Mathematics Subject Classification (2010)

MSC 90C15 MSC 90C30 

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Notes

Acknowledgements

The authors gratefully acknowledge the PGMO project “Optimisation sous contraintes de fiabilité de systèmes complexes - Application à l’ancrage des supports d’éolienne flottante” through which part of this work was funded. The authors would also like to thank two anonymous referees whose evaluation was greatly appreciated.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.EDF R&D, OSIRISPalaiseauFrance
  2. 2.IFP Energies nouvellesRueil MalmaisonFrance

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