Geometry and Symmetry in Non-Convex Optimization

This lecture explores the role of geometry and symmetry in non-convex optimization, focusing on benign non-convexity and its implications in various optimization problems such as principal component analysis, low-rank matrix completion, and community detection. The instructor delves into the concept of symmetry complexifying the landscape without necessarily making the problem hard, highlighting the importance of Riemannian optimization in computing second-order stationary points on smooth manifolds.