Multivariate exponential integral approximations: a moment approach

Dimitris Bertsimas(dbertsimmit.edu)
Xuan Vinh Doan(vanxuanmit.edu)
Jean Lasserre(lasserrelaas.fr)

Abstract: We propose a method to approximate a class of exponential multivariate integrals using moment relaxations. Using this approach, both lower and upper bounds of the integrals are obtained and we show that these bound values asymptotically converge to the real value of the integrals when the moment degree r increases. We further demonstrate the method by calculating both hypercubic and order statistic probabilities for multivariate normal distributions.

Keywords: moment relaxation, multivariate integral

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: January 2007

Download: [PDF]

Entry Submitted: 02/19/2007
Entry Accepted: 02/19/2007
Entry Last Modified: 02/19/2007

Modify/Update this entry