Resumen:
Given a parameter-dependent random inequality system a probability function assigns to the parameter the probability of satisfying this system. Such functions play a fundamental role in defining so-called probabilistic or chance constraints as they arise in numerous engineering problems (e.g. hydro reservoir management under uncertain inflows or gas network managment under uncertain demand).
Probability functions exhibit some inherent nonsmoothness even if the input data (random inequality system and density of the random distribution) are smooth. Hence the application of tools from nonsmooth and variational analysis comes as a natural consequence. The talk discusses (sub-)differentiabilty of probability functions and discusses some application to power management.