Trust Region Methods: Why, with an Example

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Explores practical aspects of Riemannian trust-region optimization and introduces the truncated conjugate gradient method.

Explores geodesic convexity, focusing on properties of convex functions on manifolds.

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

Discusses the gradient method for optimization, focusing on its application in machine learning and the conditions for convergence.

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

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

Covers non-convex optimization techniques and their applications in machine learning.

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

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

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