Lecture summary: optimization on manifolds

The course (EPFL-512) was given at EPFL in the summer semester 2025 by Professor Nicolas Boumal and Andreea Musat, see course website.

Contents:

  • Applications of optimization on manifolds
  • First-order Riemannian geometry in Euclidean spaces
  • First-order optimization algorithms on manifolds
  • Second-order Riemannian geometry in Euclidean spaces
  • Second-order optimization algorithms on manifolds
  • General framework of differential geometry
  • Optimization on non-smooth domains
  • Geodesic convexity

Disclaimer: The following lecture notes were written by Markus Renoldner. They may contain typos or mistakes; any such errors are the author’s responsibility.

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