Optimization on Manifolds

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Related lectures (32)

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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.

Differential Forms on Manifolds

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

Optimization on Manifolds: Context and Applications

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

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.

Riemannian metrics and gradients: Examples and Riemannian submanifolds

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

Manifolds and Tangent Space

Introduces manifolds, charts, atlases, tangent space, tensors, and the metric in curved spaces.

Riemannian connections: What they are and why we care

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Riemannian connections

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

Connections: motivation and definition

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