Conjugate Functions: Dual Programs

This lecture covers the concept of conjugate functions, focusing on defining a dual function of a given function f: RM -> R. The dual function is denoted as f*: R^m -> R and preserves information about f when it is convex. The lecture also discusses examples of conjugate functions, dual programs, and the optimization problem domain. It explains the process of rescaling and provides insights into convex programs, convex functions, and the proof of local optimum solutions. Additionally, it explores the observation that the dual program is convex and the application of convex programs in optimization problems.