Combinatorial Optimization with Information Geometry: The Newton Method

Entropy

Luigi Malagò¹ 

[1] Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico, 39/41, 20135 Milano, Italy; E-Mail:

关键词: statistical manifold;    Riemannian Hessian;    combinatorial optimization;    Newton method;   

DOI  :  10.3390/e16084260

来源: mdpi

【 摘 要 】

We discuss the use of the Newton method in the computation of max(p ↦ [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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland