Computing the Newton Step: GD as a Matrix-Free Way

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Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

Hands on with Manopt

Explores practical optimization using Manopt for manifolds, covering gradient checks, approximation errors, and Hessian computations.

Connections: motivation and definition

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

Differential Forms on Manifolds

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

Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.

RTR practical aspects + tCG

Explores practical aspects of Riemannian trust-region optimization and introduces the truncated conjugate gradient method.

Gradient Descent

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

Geodesic convexity: why, and what we need

Explores geodesic convexity and its extension to optimization on manifolds, emphasizing the preservation of the key fact that local minima imply global minima.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Connections: Axiomatic Definition

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.