Conjugate Duality: Envelope Representations and Subgradients

This lecture covers the concept of conjugate duality in convex optimization, focusing on envelope representations and subgradients. It explains the theorems related to proper, convex, and closed functions, such as the pointwise supremum of affine functions and supporting hyperplanes. The lecture also delves into the definition of subgradients and the subdifferential of a function. Key takeaways include the understanding of conjugate functions, the biconjugate, and the duality gap in optimization problems.