The following preface from the text should give a good indication of the level, prerequisites and ambit of the course.
Optimization is a rich and thriving mathematical discipline.
Properties of minimizers and maximizers of functions rely intimately on a wealth of techniques from mathematical analysis, including tools from calculus and its generalizations, topological notions, and more geometric ideas. The powerful and elegant language of convex analysis unifies much of this theory. Hence our aim of writing a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. For students of optimization and analysis, there is great benefit to blurring the distinction between the two disciplines. Good reference works on finite-dimensional convex analysis already exist.