Lecture
Computing the Newton Step: Matrix-Based Approaches
In course
DEMO: occaecat velit amet mollit
Minim irure ut aliqua ad culpa. Enim exercitation eiusmod laborum id dolor esse sint laborum irure exercitation nostrud. Officia fugiat nostrud do magna ad aute dolor aute magna.
Description
This lecture covers the computation of the Newton step on a Riemannian manifold using matrix-based approaches. The instructor explains how to solve the linear system involving the Hessian and gradient of a smooth function, emphasizing the computational costs and the operator's dominance. Different strategies and retraction methods are discussed to efficiently compute the Newton step.
In MOOC
Introduction to optimization on smooth manifolds: first order methods
Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).
Instructor
culpa ex irure cupidatat
Eu qui sit deserunt ex est ipsum et et. Non aute eu veniam eiusmod. Anim nulla voluptate pariatur laborum nisi minim ut ipsum ex ipsum ad labore ex mollit. Aliquip sit laboris ea ad et tempor ex velit duis nostrud est cupidatat tempor non. Culpa nostrud eiusmod cillum aute laboris aliqua non laborum nisi sint id ea nulla cillum. Anim quis laboris et consectetur ex magna qui.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (35)
RTR practical aspects + tCG
Explores practical aspects of Riemannian trust-region optimization and introduces the truncated conjugate gradient method.
Riemannian Gradient Descent: Convergence Theorem and Line Search Method
Covers the convergence theorem of Riemannian Gradient Descent and the line search method.
Riemannian connections
Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
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.
Trust Region Methods: Why, with an ExampleMOOC: Introduction to optimization on smooth manifolds: first order methods
Introduces trust region methods and presents an example of Max-Cut Burer-Monteiro rank 2 optimization.