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POPULATION-BASED OPTIMIZATION ON RIEMANNIAN MANIFOLDS IBD

PETER TINO / ROBERT SIMON FONG
SPRINGER
05 / 2022
9783031042928
Inglés

Sinopsis

Manifold optimization is an emerging field of contemporary optimization thatáconstructs efficient and robust algorithms by exploiting the specific geometricalástructure of the search space. In our case the search space takes the form of aámanifold.áManifold optimization methods mainly focus on adapting existing optimizationámethods from the usual 'easy-to-deal-with' Euclidean search spaces to manifoldsáwhose local geometry can be defined e.g. by a Riemannian structure. In this wayáthe form of the adapted algorithms can stay unchanged. However, to accommodateáthe adaptation process, assumptions on the search space manifold often have toábe made. In addition, the computations and estimations are confined by the localágeometry.This book presents a framework for population-based optimization on Riemannianámanifolds that overcomes both the constraints of locality and additional assumptions.áMulti-modal, black-box manifold optimization problems on Riemannian manifoldsácan be tackled using zero-order stochastic optimization methods from a geometricaláperspective, utilizing both the statistical geometry of the decision spaceáand Riemannian geometry of the search space.This monograph presents in a self-contained manner both theoretical and empiricaláaspects ofástochastic population-based optimization on abstract Riemannianámanifolds.