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

被引：2

作者：

Hong L.J. ^{[1
]}

Jiang G.-X. ^{[2
]}

机构：

[1] Department of Economics and Finance and Department of Management Sciences, City University of Hong Kong

[2] Department of Economics and Finance, City University of Hong Kong

来源：

Journal of the Operations Research Society of China | 2017年 / 5卷 / 4期

关键词：

Chance-constrained program; Gradient estimation; Monte Carlo simulation;

D O I：

10.1007/s40305-017-0154-6

中图分类号：

学科分类号：

摘要：

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. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.

引用

页码：431 / 455

页数：24

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