Linear convergence with Polyak-Łojasiewicz: Mechanical proof

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 2 of 4

Covers geodesically convex optimization on Riemannian manifolds, exploring convexity properties and minimization relationships.

Optimization on Manifolds

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

Riemannian metrics and gradients: Why and definition of Riemannian manifolds

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Riemannian distance, geodesically convex sets

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Taylor expansions: second order

Explores Taylor expansions and retractions on Riemannian manifolds, emphasizing second-order approximations and covariant derivatives.

Computing the Newton Step: Matrix-Based Approaches

Explores matrix-based approaches for computing the Newton step on a Riemannian manifold.

Riemannian Hessians: Definition and Example

Covers the definition and computation of Riemannian Hessians on manifolds.

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.

Newton's method on Riemannian manifolds

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic 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.