Geodesic Convexity: Basic Facts and Definitions

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (35)

Riemannian distance, geodesically convex sets Log in to Mediaspace to watch this video

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

Riemannian connections Log in to Mediaspace to watch this video

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

Riemannian Gradient Descent: Convergence Theorem and Line Search Method Log in to Mediaspace to watch this video

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

RTR practical aspects + tCG Log in to Mediaspace to watch this video

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

Optimization on Manifolds Log in to Mediaspace to watch this video

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

Manopt: Optimization Toolbox for Manifolds Log in to Mediaspace to watch this video

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Convex Optimization: Convex Functions Log in to Mediaspace to watch this video

Covers the concept of convex functions and their applications in optimization problems.

Optimization Techniques: Convexity and Algorithms in Machine Learning Log in to Mediaspace to watch this video

Covers optimization techniques in machine learning, focusing on convexity, algorithms, and their applications in ensuring efficient convergence to global minima.

Symmetry Property: Riemannian Connection in Geometry Log in to Mediaspace to watch this video

Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.

Convex Functions Log in to Mediaspace to watch this video

Covers the properties and operations of convex functions.

Newton's method on Riemannian manifolds Log in to Mediaspace to watch this video

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

Optimal Transport: Convexity and Inequalities Log in to Mediaspace to watch this video

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Isoperimetric Inequality: Optimal Transport Log in to Mediaspace to watch this video

Explores the isoperimetric inequality and its application in optimal transport, discussing properties of optimal maps and quality cases.

Differential of a Morphism Log in to Mediaspace to watch this video

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

Stationary Points and Saddle Points Log in to Mediaspace to watch this video

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

Page 2 of 2