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.
Entry Submitted: 08/28/2007
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