Geodesic Convexity: Basic Definitions

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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.