Next Article in Journal
“Lagrangian Temperature”: Derivation and Physical Meaning for Systems Described by Kappa Distributions
Previous Article in Journal
Thermoeconomic Evaluation of Integrated Solar Combined Cycle Systems (ISCCS)
Previous Article in Special Issue
Network Decomposition and Complexity Measures: An Information Geometrical Approach
Entropy 2014, 16(8), 4260-4289; doi:10.3390/e16084260

Combinatorial Optimization with Information Geometry: The Newton Method

1 Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico, 39/41, 20135 Milano, Italy 2 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.
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) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
MDPI and ACS Style

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

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here


Cited By

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert