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

Combinatorial Optimization with Information Geometry: The Newton Method

1
 and 2,*
Received: 31 March 2014; in revised form: 10 July 2014 / Accepted: 11 July 2014 / Published: 28 July 2014
(This article belongs to the Special Issue Information Geometry)
Abstract: 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.
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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Malagò L, Pistone G. Combinatorial Optimization with Information Geometry: The Newton Method. Entropy. 2014; 16(8):4260-4289.

Chicago/Turabian Style

Malagò, Luigi; Pistone, Giovanni. 2014. "Combinatorial Optimization with Information Geometry: The Newton Method." Entropy 16, no. 8: 4260-4289.


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