Subdifferential characterization of probability functions under Gaussian distribution
暂无分享,去创建一个
[1] René Henrion,et al. On the quantification of nomination feasibility in stationary gas networks with random load , 2016, Math. Methods Oper. Res..
[2] A. Kruger. On Fréchet Subdifferentials , 2003 .
[3] S. Uryasev. Derivatives of probability functions and integrals over sets given by inequalities , 1994 .
[4] Henrik O. Madsen,et al. Structural Reliability Methods , 1996 .
[5] A. Genz,et al. Computation of Multivariate Normal and t Probabilities , 2009 .
[6] René Henrion,et al. A joint model of probabilistic/robust constraints for gas transport management in stationary networks , 2017, Comput. Manag. Sci..
[7] Ian H. Sloan,et al. QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere , 2012, Math. Comput..
[8] J Figueira,et al. Stochastic Programming , 1998, J. Oper. Res. Soc..
[9] René Henrion,et al. Gradient Formulae for Nonlinear Probabilistic Constraints with Gaussian and Gaussian-Like Distributions , 2014, SIAM J. Optim..
[10] István Deák. Subroutines for Computing Normal Probabilities of Sets—Computer Experiences , 2000, Ann. Oper. Res..
[11] B. Mordukhovich. Variational analysis and generalized differentiation , 2006 .
[12] R. Wets,et al. Stochastic programming , 1989 .
[13] C. Castaing,et al. Convex analysis and measurable multifunctions , 1977 .
[14] A. I. Kibzun,et al. Differentiability of probability function , 1998 .
[15] René Henrion,et al. (Sub-)Gradient Formulae for Probability Functions of Random Inequality Systems under Gaussian Distribution , 2017, SIAM/ASA J. Uncertain. Quantification.
[16] Patrizia Pucci,et al. A representation theorem for Aumann integrals , 1984 .
[17] René Henrion,et al. Feasibility of nominations in stationary gas networks with random load , 2015 .
[18] Georg Ch. Pflug,et al. Probability Gradient Estimation by Set-Valued Calculus and Applications in Network Design , 2005, SIAM J. Optim..
[19] Abderrahim Hantoute,et al. Sequential and exact formulae for the subdifferential of nonconvex integral functionals , 2018, 1803.05521.
[20] I. Ekeland. Review: C. Castaing and M. Valadier, Convex analysis and measurable multifunctions , 1978 .
[21] Bastian Goldlücke,et al. Variational Analysis , 2014, Computer Vision, A Reference Guide.
[22] F. Clarke. Optimization And Nonsmooth Analysis , 1983 .