Derivatives of probability functions and integrals over sets given by inequalities

DOI10.1016/0377-0427(94)90388-3zbMath0826.60054OpenAlexW2093304942MaRDI QIDQ1893972

Stanislav P. Uryasev

Publication date: 7 August 1995

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(94)90388-3

zbMATH Keywords

chance-constrained programminggradient of probability functions

Mathematics Subject Classification ID

Stochastic analysis (60H99)

Related Items (16)

Differentiability conditions for stochastic hybrid systems with application to the optimal design of microgrids ⋮ A discussion of probability functions and constraints from a variational perspective ⋮ Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization ⋮ Derivatives of probability functions: unions of polyhedra and elliptical distributions ⋮ Eventual convexity of probability constraints with elliptical distributions ⋮ Probability maximization via Minkowski functionals: convex representations and tractable resolution ⋮ (Sub-)differentiability of probability functions with elliptical distributions ⋮ A characterization of the subdifferential of singular Gaussian distribution functions ⋮ Subdifferential characterization of probability functions under Gaussian distribution ⋮ Gradient formulae for nonlinear probabilistic constraints with non-convex quadratic forms ⋮ Differentiability and semismoothness properties of integral functions and their applications ⋮ Generalized Differentiation of Probability Functions Acting on an Infinite System of Constraints ⋮ Rectangular chance constrained geometric optimization ⋮ Differentiability of probability function ⋮ (Sub-)Gradient Formulae for Probability Functions of Random Inequality Systems under Gaussian Distribution ⋮ Generalized differentiation of probability functions: parameter dependent sets given by intersections of convex sets and complements of convex sets

Cites Work

• Version-Independence and Nested Distributions in Multistage Stochastic Optimization
• stochastic quasigradient methods and their application to system optimization^†
• Differentiability of the integral over a set defined by inclusion
• A differentiation formula for integrals overseas given by inclusion
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