RTR practical aspects + tCG

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Related lectures (30)

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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.

Riemannian connections

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

Optimality Conditions: First Order

Covers optimality conditions in optimization on manifolds, focusing on global and local minimum points.

Computing the Newton Step: Matrix-Based Approaches

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

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.

Descent methods and line search: Finiteness of the line search algorithm

Explores the Wolfe conditions for line search algorithms and proves the finiteness of the line search parameter.

Geodesically Convex Optimization

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

Gradient Descent

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

Optimization without Constraints: Gradient Method

Covers optimization without constraints using the gradient method to find the function's minimum.

Riemannian Hessians: Definition and Example

Covers the definition and computation of Riemannian Hessians on manifolds.