We consider the classical problem of estimating a density on $[0,1]$ via some maximum entropy criterion. For solving this convex optimization problem with algorithms using first-order or second-order methods, at each iteration one has to compute (or at least approximate) moments of some measure with a density on $[0,1]$, to obtain gradient and Hessian data. We propose a numerical scheme based on semidefinite programming that avoids computing quadrature formula for this gradient and Hessian computation.
Citation
To appear in Proceedings of the 46th IEEE CDC Conference, New Orleans, December 2007.
Article
View Semidefinite Programming for Gradient and Hessian Computation in Maximum Entropy Estimation