T�tulo: Population-Based Optimization on Riemannian Manifolds (Studies in Computational Intelligence, 1046)
Editor: Springer
Fecha de publicaci�n: 2022
Idioma: Ingl�s
ISBN 10: 3031042921
ISBN 13: 9783031042928
Encuadernaci�n: Encuadernaci�n de tapa dura
Estado: New

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Sinopsis

Manifold optimization is an emerging field of contemporary optimization that constructs efficient and robust algorithms by exploiting the specific geometrical structure of the search space. In our case the search space takes the form of a manifold.

Manifold optimization methods mainly focus on adapting existing optimization methods from the usual "easy-to-deal-with" Euclidean search spaces to manifolds whose local geometry can be defined e.g. by a Riemannian structure. In this way the form of the adapted algorithms can stay unchanged. However, to accommodate the adaptation process, assumptions on the search space manifold often have to be made. In addition, the computations and estimations are confined by the local geometry.

This book presents a framework for population-based optimization on Riemannian manifolds that overcomes both the constraints of locality and additional assumptions. Multi-modal, black-box manifold optimization problems on Riemannian manifolds can be tackled using zero-order stochastic optimization methods from a geometrical perspective, utilizing both the statistical geometry of the decision space and Riemannian geometry of the search space.

This monograph presents in a self-contained manner both theoretical and empirical aspects of stochastic population-based optimization on abstract Riemannian manifolds.

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Charlotte y Peter Fiell son dos autoridades en historia, teor�a y cr�tica del dise�o y han escrito m�s de sesenta libros sobre la materia, muchos de los cuales se han convertido en �xitos de ventas. Tambi�n han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Dise�o del siglo XX, El dise�o industrial de la A a la Z, Scandinavian Design y Dise�o del siglo XXI.

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