Derivatives of probability functions and integrals over sets given by inequalities

Stanislav Uryas'ev

doi:10.1016/0377-0427(94)90388-3

Derivatives of probability functions and integrals over sets given by inequalities

Stanislav Uryas'ev

Applied Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

Probability functions, depending upon their parameters, are reduced to integrals calculated over sets given by many inequalities. A new general formula for the differentiation of such integrals is proposed. A gradient of the integral is represented as the sum of integrals taken over a volume and over a surface. These results are used to calculate the sensitivities of probability functions, and also for chance-constrained optimization.

Original language	English
Pages (from-to)	197-223
Number of pages	27
Journal	Journal of Computational and Applied Mathematics
Volume	56
Issue number	1-2
DOIs	https://doi.org/10.1016/0377-0427(94)90388-3
State	Published - Dec 20 1994

Keywords

Integral derivatives
Probability derivatives

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10.1016/0377-0427(94)90388-3

Cite this

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title = "Derivatives of probability functions and integrals over sets given by inequalities",

abstract = "Probability functions, depending upon their parameters, are reduced to integrals calculated over sets given by many inequalities. A new general formula for the differentiation of such integrals is proposed. A gradient of the integral is represented as the sum of integrals taken over a volume and over a surface. These results are used to calculate the sensitivities of probability functions, and also for chance-constrained optimization.",

keywords = "Integral derivatives, Probability derivatives",

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AU - Uryas'ev, Stanislav

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Y1 - 1994/12/20

N2 - Probability functions, depending upon their parameters, are reduced to integrals calculated over sets given by many inequalities. A new general formula for the differentiation of such integrals is proposed. A gradient of the integral is represented as the sum of integrals taken over a volume and over a surface. These results are used to calculate the sensitivities of probability functions, and also for chance-constrained optimization.

AB - Probability functions, depending upon their parameters, are reduced to integrals calculated over sets given by many inequalities. A new general formula for the differentiation of such integrals is proposed. A gradient of the integral is represented as the sum of integrals taken over a volume and over a surface. These results are used to calculate the sensitivities of probability functions, and also for chance-constrained optimization.

KW - Integral derivatives

KW - Probability derivatives

UR - https://www.scopus.com/pages/publications/0040553301

U2 - 10.1016/0377-0427(94)90388-3

DO - 10.1016/0377-0427(94)90388-3

M3 - Article

AN - SCOPUS:0040553301

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VL - 56

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EP - 223

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

Derivatives of probability functions and integrals over sets given by inequalities

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Keywords

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