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(Sub-) Gradient formulae for probability functions of random inequality systems under Gaussian distribution

Submission Status:published
  • We consider probability functions of parameter-dependent random inequality systems under Gaussian distribution. As a main result, we provide an upper estimate for the Clarke subdifferential of such probability functions without imposing compactness conditions. A constraint qualification ensuring continuous differentiability is formulated. Explicit formulae are derived from the general result in case of linear random inequality systems. In the case of a constant coefficient matrix an upper estimate for even the smaller Mordukhovich subdifferential is proven.

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Metadaten
Author:Wim van Ackooij, Rene Henrion
DOI:https://doi.org/10.1137/16M1061308
Parent Title (English):SIAM/ASA J. Uncertainty Quantification
Document Type:Article
Language:English
Date of Publication (online):2017/01/10
Date of first Publication:2017/01/10
Release Date:2016/11/28
Volume:5
First Page:63
Last Page:87
Institutes:Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B04