Convex Functions: Theory and Applications

This lecture covers the concept of convex functions, starting with the definition and checking convexity along lines. It explores the convexity of the negative log-determinant function and convexity-preserving transformations. The lecture delves into affine transformations, pointwise maximum and supremum, piecewise linear functions, and the maximum eigenvalue function. It also discusses composition of convex functions, concave functions, and generalizations. The lecture concludes with topics on minimization, Schur's Lemma, distance function to a convex set, perspective function, and relative entropy.