Hands on with Manopt: Optimization on Manifolds

This lecture introduces Manopt, a Matlab toolbox for optimization on manifolds, focusing on smooth manifolds with a Riemannian structure. It covers the types of cost functions and manifolds that Manopt can handle, as well as the general principles of the toolbox. The lecture also provides examples of different types of manifolds, such as Euclidean spaces, spheres, Stiefel and Grassmann manifolds, and fixed-rank matrices. Additionally, it explains how to specify an optimization problem using Manopt and describes the process of moving around the manifold following tangent vectors. The lecture concludes with practical examples and demonstrations of using Manopt for optimization problems.