# Resources to learn optimization on manifolds

The documentation on this website is meant to help users get to grips with Manopt. Underneath the software, there is a fair amount of math. This page provides some pointers to learn that theory.

### Books

The following books (both available online for free) can be helpful to learn the relevant mathematics:

An introduction to optimization on smooth manifolds

Nicolas Boumal, Cambridge University Press, 2023.

Optimization algorithms on matrix manifolds

Pierre-Antoine Absil, Robert Mahony and Rodolphe Sepulchre, Princeton University Press, 2008.

### A full course

- MATH-512 at EPFL: this is a full set of
**video lectures**, slides and exercises (with hints and solutions). - edX course: this covers the first six weeks of MATH-512, on the edX platform.

### Tutorial videos

- This one-hour video and this two-hour video introduce the basics of differential geometry and Riemannian geometry for optimization on smooth manifolds. They cover more or less the same contents. The slides have been augmented for a longer in-person tutorial.
- Week 5 of MATH-512 includes a lecture about Manopt: the basics and a bit more.

### Blogs and blog posts

- The Race to the bottom blog about nonconvex optimization features some Riemannian optimization.
- This blog post gives an informal overview of optimization on manifolds.

### Code examples

- See the examples that ship with Manopt.