Population-Based Optimization on Riemannian Manifolds

Peter Tino

ISBN 10: 3031042956 / ISBN 13: 9783031042959

Verlag: Springer International Publishing, Springer International Publishing, 2023

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - Manifold optimization is an emerging field of contemporary optimization thatconstructs efficient and robust algorithms by exploiting the specific geometricalstructure of the search space. In our case the search space takes the form of amanifold.Manifold optimization methods mainly focus on adapting existing optimizationmethods from the usual 'easy-to-deal-with' Euclidean search spaces to manifoldswhose local geometry can be defined e.g. by a Riemannian structure. In this waythe form of the adapted algorithms can stay unchanged. However, to accommodatethe adaptation process, assumptions on the search space manifold often have tobe made. In addition, the computations and estimations are confined by the localgeometry.This book presents a framework for population-based optimization on Riemannianmanifolds that overcomes both the constraints of locality and additional assumptions.Multi-modal, black-box manifold optimization problems on Riemannian manifoldscan be tackled using zero-order stochastic optimization methods from a geometricalperspective, utilizing both the statistical geometry of the decision spaceand Riemannian geometry of the search space.This monograph presents in a self-contained manner both theoretical and empiricalaspects ofstochastic population-based optimization on abstract Riemannianmanifolds.

Bestandsnummer des Verkäufers 9783031042959

Bibliografische Details

• Titel: Population-Based Optimization on Riemannian Manifolds
• Verlag: Springer International Publishing, Springer International Publishing
• Erscheinungsjahr: 2023
• Sprache: Englisch
• ISBN-10: 3031042956
• ISBN-13: 9783031042959
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 11 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 11 mm
• Gewicht: 283 Gramm

Über diesen Titel

Inhaltsangabe

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.