GRADIENT FORMULAE FOR NONLINEAR PROBABILISTIC CONSTRAINTS WITH GAUSSIAN AND GAUSSIAN-LIKE DISTRIBUTIONS ∗

摘要: Probabilistic constraints represent a major model of stochastic optimization. A possible approach for solving probabilistically constrained optimization problems consists in applying nonlinear programming methods. To do so, one has to provide sufficiently precise approximations values and gradients probability functions. For linear probabilistic under Gaussian distribution this can be done successfully by analytically reducing these functions computing the latter, instance, Genz's code. models may fall back on spherical-radial decomposition random vectors apply, Deak's sampling scheme uniform sphere order compute corresponding The present paper demonstrates how same used simultaneously More precisely, we prove formula repre...