Population-Based Optimization on Riemannian Manifolds

Manifold optimization is a new area of optimization that develops efficient and robust algorithms by taking advantage of the geometrical structure of the search space. This book provides a framework for population-based optimization on Riemannian manifolds that overcomes the constraints of locality and additional assumptions, allowing for multi-modal, black-box manifold optimization problems to be tackled.

Format: Hardback
Length: 168 pages
Publication date: 18 May 2022
Publisher: Springer International Publishing AG

Manifold optimization is a rapidly evolving area of contemporary optimization that harnesses the inherent geometric structure of the search space to develop efficient and robust algorithms. In our specific case, the search space assumes the form of a manifold.

Manifold optimization techniques primarily aim to adapt conventional optimization methods from Euclidean search spaces, which are typically easier to handle, to manifolds characterized by local geometries defined, for instance, by Riemannian structures. By preserving the form of the adapted algorithms, this approach ensures their stability. However, accommodating the adaptation process often necessitates assumptions about the manifold's geometry. Additionally, the computations and estimations are constrained by the local geometry.

This book offers a comprehensive framework for population-based optimization on Riemannian manifolds, addressing both the limitations of locality and additional assumptions. It enables the solution of multi-modal, black-box manifold optimization problems using zero-order stochastic optimization methods from a geometrical perspective. By leveraging the statistical geometry of the decision space and the Riemannian geometry of the search space, these methods offer a novel approach to tackling complex optimization challenges on abstract Riemannian manifolds.

The monograph comprehensively presents both theoretical and empirical aspects of stochastic population-based optimization on abstract Riemannian manifolds, providing a self-contained resource for researchers and practitioners in this field.

Weight: 442g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031042928
Edition number: 1st ed. 2022