Lectures related to Choosing a Step Size

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

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

Explores matrix-based and matrix-free approaches for computing the Newton step in optimization 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.

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.

Truncated Conjugate Gradients for Trust-Region Subproblem

Explores truncated conjugate gradients for solving the trust-region subproblem in optimization on manifolds efficiently.

Computing the Newton Step: From GD to CG

Covers the transition from Gradient Descent to Conjugate Gradients, highlighting the efficiency of CG over GD in optimization on manifolds.

Optimality conditions: second order

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

Hands on with Manopt MOOC: Introduction to optimization on smooth manifolds: first order methods

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

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.

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.

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.

Optimization: Gradient Descent and Subgradients

Explores optimization methods like gradient descent and subgradients for training machine learning models, including advanced techniques like Adam optimization.

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.

Connections: Axiomatic Definition

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

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.

Topology of Riemann Surfaces

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

Optimization on Manifolds Log in to Mediaspace to watch this video

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

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.

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

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