Population-based Optimization on Riemannian Manifolds

Robert Simon Fong|Peter Tino

ISBN 10: 3031042921 / ISBN 13: 9783031042928

Editore: Springer International Publishing, 2022

Riguardo questo articolo

Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Presents recent research on Population-based Optimization on Riemannian manifolds Addresses the locality and implicit assumptions of manifold optimization Presents a novel population-based optimization algorithm on Riemannian manifolds .

Codice articolo 575523153

Dati bibliografici

• Titolo: Population-based Optimization on Riemannian Manifolds
• Editore: Springer International Publishing
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 3031042921
• ISBN 13: 9783031042928
• Rilegatura: Rilegato
• Condizione: New
• Cataloghi dei venditori:
  • Mathematik/Naturwissenschaften/Technik/Medizin

Descrizione articolo

Riassunto

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.