Convex Optimization: Sets and Functions

This lecture covers the fundamental concepts of convex optimization, focusing on convex sets and functions. It starts by defining convex sets and their properties, such as intersections and convex functions. Examples of convex functions in one variable are provided, along with operations on convex functions. The lecture also delves into the gradient and Hessian of convex functions, discussing necessary and sufficient conditions for convexity. Real-world applications of convex optimization, such as portfolio management and traffic management, are highlighted, emphasizing the wide applicability of these concepts.