Geodesic Convexity: Basic Facts and Definitions

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Geodesic Convexity: Basic Definitions

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Geodesically Convex Optimization

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

Trust Region Methods: Why, with an Example

Introduces trust region methods and presents an example of Max-Cut Burer-Monteiro rank 2 optimization.

Optimization on Manifolds: Context and Applications

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Riemannian distance, geodesically convex sets

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

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.

Linear convergence with Polyak-Łojasiewicz: Mechanical proof

Explores linear convergence with the Polyak-Łojasiewicz condition on a Riemannian manifold.

Riemannian Gradient Descent: Convergence Theorem and Line Search Method

Covers the convergence theorem of Riemannian Gradient Descent and the line search method.

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.