Geodesic convexity: why, and what we need

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 1 of 4

Smooth Manifolds: Diffeomorphisms

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

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.

Optimization on Manifolds

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

Convexity: Functions and Global Minima

Explores convex functions, global minima, and their relationship with differentiability.

Hessians, Symmetry and Examples: Sphere, Stiefel

Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.

Comparing Tangent Vectors: Parallel Transport

Explores comparing tangent vectors and parallel transport on manifolds.

Transporters: a proxy for parallel transport

Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.

Gradients on Riemannian submanifolds, local frames

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

Riemannian connections

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

Optimization on Manifolds: Context and Applications

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