Ebook: Optimization algorithms on matrix manifolds

Foreword / by Paul van Dooren -- Notation conventions -- Motivation and applications -- Matrix manifolds : first-order geometry -- Line-search algorithms on manifolds -- Matrix manifolds : second-order geometry -- Newton's method -- Trust-region methods -- A constellation of superlinear algorithms -- Elements of linear algebra, topology, and calculus.;Many problems in the sciences and engineering can be rephrased as optimisation problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms.