(Sub-) Gradient formulae for probability functions of random inequality systems under Gaussian distribution
Submission Status: | published |
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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 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.