Optimization Duality: Theory and Algorithms

This lecture covers the theory of optimization duality, focusing on the minimax formulation and its dual problem. It explains the concept of weak duality, concavity of the dual problem, and the conditions for strong duality. The lecture also delves into the practical aspects of optimization algorithms, discussing the numerical accuracy, e-accuracy, and the primal-dual gap function. Furthermore, it explores the application of gradient descent-ascent algorithms for minimax optimization and the challenges in nonconvex-concave problems. The lecture concludes with a glimpse into algorithms that converge and encourages students to complete their homework.