Abstract:

Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously. It appears naturally in chanceconstrained 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.

Key words: Chance-constrained program ·, Gradient estimation ·, Monte Carlo simulation