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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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Original languageEnglish
Pages (from-to)431-455
Journal / PublicationJournal of the Operations Research Society of China
Issue number4
Early online date13 Mar 2017
Publication statusPublished - Dec 2017


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.

Research Area(s)

  • Chance-constrained program, Gradient estimation, Monte Carlo simulation