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.


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

An introduction to optimization on smooth manifolds An introduction to optimization on smooth manifolds
Nicolas Boumal, Cambridge University Press, 2023.

Optimization algorithms on matrix manifolds 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.