Retractions vector fields and tangent bundles: Tangent bundles

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

From embedded to general manifolds: Why?

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Smooth Manifolds: Diffeomorphisms

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.

Differentiating Vector Fields: How Not to Do It

Discusses the challenges in differentiating vector fields on submanifolds and the importance of choosing the right method.

All things Riemannian: metrics, (sub)manifolds and gradients

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

Covariant derivatives along curves

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

Linear Lie Groups: Definitions and Theorems

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

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Manopt: Optimization Toolbox for Manifolds

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

Comparing Tangent Vectors: Parallel Transport

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

Hands on with Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.