Convex Optimization

This lecture covers the basics of optimization, focusing on minimizing a function over a vector space. The instructor explains the concept of convexity, the properties of convex functions, and the relationship between convex functions and their epigraphs. The lecture also delves into the importance of convex optimization in finding local and global minima, showcasing the power of convexity in simplifying the minimization process and ensuring optimality. Additionally, the instructor demonstrates how to prove convexity using linear approximations and compositions of convex functions.