Lectures related to Geodesic Convexity: Basic Definitions

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

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

Covers the properties and operations of convex functions.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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

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

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

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Covers exercises on convex optimization, focusing on formulating and solving optimization problems using YALMIP and solvers like GUROBI and MOSEK.

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Explores convexity, Jacobians, subdifferentials, and convergence rates in optimization and function analysis.

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.

Discusses the theorems on convex functions and provides examples for better understanding.

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

Discusses local extrema of functions in two variables around the point (0,0).

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

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

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

Covers calculating with Taylor series and convexity concepts, including sin(x) and cos(x) approximations.