Newton's method on Riemannian manifolds

Related lectures (32)

Page 3 of 4

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Explores gradient descent methods for optimizing functions on manifolds, emphasizing small gradient guarantees and global convergence.

Introduces trust region methods and presents an example of Max-Cut Burer-Monteiro rank 2 optimization.

Covers the concept of local frames, their construction, and limitations.

Explores the definition of connections for smooth vector fields on manifolds.

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.

Covers the definition and computation of Riemannian Hessians on manifolds.