This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Ackooij, Wim vanHenrion, René2016-12-132019-06-2820162198-5855https://doi.org/10.34657/3282https://oa.tib.eu/renate/handle/123456789/1648We 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.application/pdfeng510Stochastic optimizationgradients of probability functionsspheric radial decompositionmultivariate Gaussian distributionClarke subdifferentialMordukhovich subdifferentialprobabilistic constraintReport