Primal-dual Optimization

This lecture covers the mathematics of data focusing on primal-dual optimization, including minimax formulations, saddle points, local Nash equilibria, and generalized Robbins-Monro schemes. It delves into the challenges of nonconvex-nonconcave settings and the complexity of finding min-max points. The instructor explains the concept of Fenchel conjugation, the bilinear min-max template, and examples like sparse recovery and constrained formulations. The lecture also discusses the reformulation between templates, the dual problem, and the nonsmoothness of the dual function, emphasizing concavity and the exchange of min and max.