Lagrangian Duality: Theory and Applications

This lecture covers Lagrangian duality in convex optimization, starting with conic form problems and their equivalence to linear programming. It explores the relationship between convex problems and conic form problems, introducing the concept of strong duality and the significance of dual solutions. The instructor explains the Lagrangian function and its role in transforming the primal problem into a min-max problem. The lecture delves into the dual problem formulation, weak duality, and the conditions for strong duality. It also discusses the hierarchy of convex optimization problems, the dual cones concept, and practical applications of Lagrangian duality in second-order cone programs and quadratic programs.