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Entropy 2014, 16(8), 4260-4289; doi:10.3390/e16084260

Combinatorial Optimization with Information Geometry: The Newton Method

Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico, 39/41, 20135 Milano, Italy
Castro Statistics, Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy
Author to whom correspondence should be addressed.
Received: 31 March 2014 / Revised: 10 July 2014 / Accepted: 11 July 2014 / Published: 28 July 2014
(This article belongs to the Special Issue Information Geometry)


We discuss the use of the Newton method in the computation of max(p → Εp [f]), where p belongs to a statistical exponential family on a finite state space. In a number of papers, the authors have applied first order search methods based on information geometry. Second order methods have been widely used in optimization on manifolds, e.g., matrix manifolds, but appear to be new in statistical manifolds. These methods require the computation of the Riemannian Hessian in a statistical manifold. We use a non-parametric formulation of information geometry in view of further applications in the continuous state space cases, where the construction of a proper Riemannian structure is still an open problem. View Full-Text
Keywords: statistical manifold; Riemannian Hessian; combinatorial optimization; Newton method statistical manifold; Riemannian Hessian; combinatorial optimization; Newton method

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Malagò, L.; Pistone, G. Combinatorial Optimization with Information Geometry: The Newton Method. Entropy 2014, 16, 4260-4289.

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