Semidefinite Programming for Gradient and Hessian Computation in Maximum Entropy Estimation

Jean B. Lasserre(lasserrelaas.fr)

Abstract: 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.

Keywords: Density estimation; maximum entropy; moments; semidefinite programming

Category 1: Applications -- Science and Engineering

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: To appear in Proceedings of the 46th IEEE CDC Conference, New Orleans, December 2007.

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Entry Submitted: 08/28/2007
Entry Accepted: 08/28/2007
Entry Last Modified: 08/28/2007

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