Optimization Basics: Norms, Convexity, Differentiability

This lecture covers the fundamentals of optimization, including norms, convexity, differentiability, and smoothness. It delves into topics such as linear algebra, analysis, convex sets and functions, convergence rates, and gradient descent methods. The presentation progresses from defining metrics and vector norms to discussing quasi-norms, semi-norms, norm balls, and dual norms. It also explores matrix norms, Schatten q-norms, operator norms, and positive definite matrices. The lecture concludes with insights on continuity, Lipschitz continuity, differentiability, gradients, and linear approximations.