Lecture
Optimization on Manifolds: Context and Applications
Related lectures (32)
Optimization on Manifolds
Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Dynamics of Steady Euler Flows: New Results
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Riemannian connections
Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
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.
Transporters: a proxy for parallel transportMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.
Choosing a Step SizeMOOC: 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.
RTR practical aspects + tCG
Explores practical aspects of Riemannian trust-region optimization and introduces the truncated conjugate gradient method.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Comparing Tangent Vectors: Three Reasons WhyMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores the importance of comparing tangent vectors at different points using algorithms and finite differences.