Lectures related to Momentum methods and nonlinear CG

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.

Optimization on Manifolds: Context and Applications MOOC: Introduction to optimization on smooth manifolds: first order methods

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

Choosing a Step Size MOOC: Introduction to optimization on smooth manifolds: first order methods

Explores choosing a step size in optimization on manifolds, including backtracking line-search and the Armijo method.

Comparing Tangent Vectors: Three Reasons Why

Explores the importance of comparing tangent vectors at different points using algorithms and finite differences.

Taylor Expansions: First Order MOOC: Introduction to optimization on smooth manifolds: first order methods

Explores Taylor expansions of first order in optimization on manifolds.

Differential Forms on Manifolds

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

Newton's method: Optimization on manifolds

Explores Newton's method for optimizing functions on manifolds using second-order information and discusses its drawbacks and fixes.

Differentiating vector fields: Why do it?

Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.

Gradient Descent MOOC: Introduction to optimization on smooth manifolds: first order methods

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

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.

Stochastic Gradient Descent: Non-convex Optimization Techniques

Discusses Stochastic Gradient Descent and its application in non-convex optimization, focusing on convergence rates and challenges in machine learning.

Retractions vector fields and tangent bundles: Tangent bundles MOOC: Introduction to optimization on smooth manifolds: first order methods

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Algebraic Topology and Differential Geometry

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Manopt: Optimization on Manifolds Log in to Mediaspace to watch this video

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

Connections: motivation and definition Log in to Mediaspace to watch this video

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

Riemannian connections Log in to Mediaspace to watch this video

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

Optimization Techniques: Stochastic Gradient Descent and Beyond Log in to Mediaspace to watch this video

Discusses optimization techniques in machine learning, focusing on stochastic gradient descent and its applications in constrained and non-convex problems.

RTR practical aspects + tCG Log in to Mediaspace to watch this video

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

Manifolds: Charts and Compatibility Log in to Mediaspace to watch this video

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

General Manifolds and Topology Log in to Mediaspace to watch this video

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