Convex Functions: Theory and Applications

This lecture covers the fundamental concepts of convex functions, including affine, convex, and conic hulls, convexity-preserving transformations, conic inequalities, and the epigraph and domain of functions. It also delves into the conditions for convexity, such as the 1st and 2nd-order conditions, and provides examples of convex functions. The lecture concludes with a discussion on checking convexity along lines as a method to verify the convexity of multivariate functions.