Convex Functions: Theory and Applications

This lecture covers the concept of convex functions, including checking convexity along lines, the negative log-determinant function, convexity-preserving transformations, affine transformations, pointwise maximum and supremum, examples of convex functions, composition of convex functions, generalizations to concave functions, minimization problems, geometric intuition, Schur's Lemma, distance function to a convex set, perspective function, and relative entropy.