Journal
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
Volume 5, Issue 1, Pages 63-87Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1061308
Keywords
stochastic optimization; gradients of probability functions; spheric-radial decomposition; multivariate Gaussian distribution; Clarke subdifferential; Mordukhovich subdifferential; probabilistic constraint
Funding
- FMJH Program Gaspard Monge in optimization and operations research by the EDF
- Deutsche Forschungsgemeinschaft [CRC TRR 154]
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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 the 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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