Convexity and Jacobians

This lecture covers the concepts of convexity, Jacobians, and their applications in optimization. It explains the Jacobian matrix for vector-valued functions, the chain rule via Jacobians, and examples of quadratic and logistic loss functions. The lecture also delves into the convexity of sets and functions, subdifferentials, and convergence rates of sequences. It discusses strongly convex functions, Lipschitz gradients, and the properties of convex functions. The presentation concludes with examples of convergence rates and hints at advanced topics like star-convexity and invexity.