Sharpening Comparisons via Gaussian Copulas and Semidefinite Programming

摘要

A common problem in operations research involves comparing two system designs through simulation of both systems. The comparison can often be made more accurate through careful control (coupling) of the random numbers that are used in simulating each system, with common random numbers being the standard example. We describe a new approach for coupling the random-number inputs to two systems that involves generating realizations of a Gaussian random vector and then transforming the Gaussian random vector into the desired random-number inputs. We use nonlinear semidefinite programming to select the correlation matrix of the Gaussian random vector, with the goal of sharpening the comparison.