Computing the Newton Step: Matrix-Based Approaches

Related lectures (32)

Page 3 of 4

Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.

Explains Riemannian submanifolds, metrics, and gradients computation on manifolds.

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

Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.

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

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

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 gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.