Gradient and Hessian of Joint Probability Function with Applications on Chance-Constrained Programs

L. Jeff Hong; Guang Xin Jiang

doi:10.1007/s40305-017-0154-6

Gradient and Hessian of Joint Probability Function with Applications on Chance-Constrained Programs

L. Jeff Hong^*
, Guang Xin Jiang

^*Corresponding author for this work

City University of Hong Kong

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

2 Scopus citations

Abstract

Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously. It appears naturally in chance-constrained programs. In this paper, we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them. We then design a Monte Carlo algorithm, based on these estimators, to solve chance-constrained programs. Our numerical study shows that the algorithm works well, especially only with the gradient estimators.

Original language	English
Pages (from-to)	431-455
Number of pages	25
Journal	Journal of the Operations Research Society of China
Volume	5
Issue number	4
DOIs	https://doi.org/10.1007/s40305-017-0154-6
State	Published - 1 Dec 2017
Externally published	Yes

Keywords

Chance-constrained program
Gradient estimation
Monte Carlo simulation

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10.1007/s40305-017-0154-6

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title = "Gradient and Hessian of Joint Probability Function with Applications on Chance-Constrained Programs",

abstract = "Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously. It appears naturally in chance-constrained programs. In this paper, we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them. We then design a Monte Carlo algorithm, based on these estimators, to solve chance-constrained programs. Our numerical study shows that the algorithm works well, especially only with the gradient estimators.",

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author = "Hong, \{L. Jeff\} and Jiang, \{Guang Xin\}",

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AU - Hong, L. Jeff

AU - Jiang, Guang Xin

PY - 2017/12/1

Y1 - 2017/12/1

N2 - Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously. It appears naturally in chance-constrained programs. In this paper, we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them. We then design a Monte Carlo algorithm, based on these estimators, to solve chance-constrained programs. Our numerical study shows that the algorithm works well, especially only with the gradient estimators.

AB - Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously. It appears naturally in chance-constrained programs. In this paper, we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them. We then design a Monte Carlo algorithm, based on these estimators, to solve chance-constrained programs. Our numerical study shows that the algorithm works well, especially only with the gradient estimators.

KW - Chance-constrained program

KW - Gradient estimation

KW - Monte Carlo simulation

UR - https://www.scopus.com/pages/publications/85037619806

U2 - 10.1007/s40305-017-0154-6

DO - 10.1007/s40305-017-0154-6

M3 - 文章

AN - SCOPUS:85037619806

SN - 2194-668X

VL - 5

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JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

IS - 4

ER -

Gradient and Hessian of Joint Probability Function with Applications on Chance-Constrained Programs

Abstract

Keywords

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