Retractions, vector fields and tangent bundles: Retractions and vector fields

Related lectures (31)

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

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

Covers smooth maps, vector fields, and retractions on manifolds, emphasizing the importance of smoothly varying curves.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.

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

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Page 2 of 2