Riemannian Hessians: Definition and Example

Related lectures (32)

Page 3 of 4

Explores geodesic convexity, focusing on properties of convex functions on manifolds.

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

Explores matrix-based approaches for computing the Newton step on a Riemannian manifold.

Covers the convergence theorem of Riemannian Gradient Descent and the line search method.

Explores computing gradients on Riemannian manifolds through extensions and retractions, emphasizing orthogonal projectors and smooth extensions.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Covers geodesically convex optimization on Riemannian manifolds, exploring convexity properties and minimization relationships.

Discusses gradients on Riemannian submanifolds and the construction of local frames.