Subgradients and Convex Functions

This lecture covers the concept of subgradients in convex functions, focusing on scenarios where functions are non-differentiable but still exhibit convexity. The instructor explains the characterization of convexity in terms of subgradient vectors and provides examples of non-differentiable convex functions. The lecture also delves into the properties of subgradients and subdifferentials for convex functions, including Jensen's inequality and useful subdifferential expressions. Through various examples, students learn how to compute subgradients for different types of convex functions and understand the significance of these calculations in optimization problems.