Lagrangian Duality: Convex Optimization

This lecture covers Lagrangian duality in convex optimization, starting with conic form problems and semidefinite programs. It explains the equivalence between convex problems and conic form problems, introducing the Lagrangian and its role in transforming problems into min-max formulations. The dual problem is defined, weak duality is discussed, and the significance of dual solutions is highlighted. The lecture also delves into specific optimization problems like least squares, linear programs, quadratic programs, and second-order cone programs. Popular solvers for these problems are presented, providing a comprehensive overview of convex optimization techniques.