Convex Optimization

This lecture covers the fundamentals of convex optimization, including the definition of convex functions and sets, the relationship between convexity and differentiability, and the importance of structural assumptions in optimization algorithms. The instructor explains how to prove the convexity of functions using linear approximations and the epigraph definition, and highlights the significance of convexity in optimization problems. The lecture also delves into the concept of lower bounds in complexity theory and the trade-off between convergence rates and iteration costs in algorithm selection.