Primal-dual optimization: Theory and Computation

This lecture covers the mathematics of data focusing on primal-dual optimization. It starts with the conjugation of functions and properties of the Fenchel conjugate. Examples include l2-norm-squared and l1-norm. The lecture delves into primal and dual problems, strong duality, and saddle points. It discusses the quadratic penalty method, numerical accuracy, and the performance of optimization algorithms. The concepts of prox-operator, quadratic penalty, and linearized methods are explained. The lecture concludes with a practical example showcasing the performance of different algorithms in solving a nonsmooth problem.