Reference for optimization on Riemannian manifolds

Question

Can anyone recommend me a fairly good textbook on optimization on manifolds? I only managed to find this: Convex Functions and Optimization Methods on Riemannian Manifolds

It seems a bit old, nothing against it obviously the content seems ok to me, but maybe there's something more recent out there.

Ideally I'd like something like Numerical Optimization By Jorge Nocedal, Stephen Wright but translated on manifolds.

But any reference you can suggest in general is fine.

Answer 1

The book Optimization Algorithms on Matrix Manifolds, by P.-A. Absil, R. Mahoney, and Rodolphe Sepulchre is from 2007. It is significantly more challenging and less nuts and bolts oriented than :Numerical Optimization", byJorge Nocedal, Stephen Wright.

Nicolas Boumal, co-developer of the Manopt Matlab tool­box for opti­mization on manifolds, is finishing up a draft of a book "An introduction to optimization on smooth manifolds". I think it may be more mathematically accessible and concrete than "Optimization Algorithms on Matrix Manifolds".

Per http://web.math.princeton.edu/~nboumal/#book

To be available soonish: a first draft of my introductory lecture notes for optimization on smooth manifolds. In the meantime, feel free to reach out by e-mail to ask for a private PDF copy.

Answer 2

Adding to Mark L. Stone's answer, I wrote a textbook for Riemannian optimization which may address the needs you describe:

An introduction to optimization on smooth manifolds

http://www.nicolasboumal.net/book

It does not assume any prerequisites in geometry. It addresses certain aspects of practical importance for numerical implementations, such as numerical pitfalls and recommended parameter values.