Geodesic Convexity: Basic Facts and Definitions

This lecture covers the basics of geodesic convexity, focusing on the properties of geodesically convex functions on Riemannian manifolds. It explains how the pointwise maximum of g-convex functions is also g-convex, and explores the concept of geodesically convex problems. The lecture delves into the relationship between local and global minima, providing insights into the optimization on manifolds. Additionally, it discusses the properties of geodesically convex functions, including strict convexity and strong convexity. The lecture concludes with an examination of different definitions of g-convex sets and their implications for optimization strategies.