Convex analysis is a key tool in optimization and nonlinear analysis. This course covers the main topics in convex optimization, variational analysis, subdifferential calculus, duality and applications. It is open to all PhD and MSc students (code MAT540), as well as Mathematical Engineering students (code MAT410) having some background in topological vector spaces, Hahn-Banach Theorem and its consequences, and weak topologies. Having taken a course in Functional Analysis is not mandatory but recommended.
J. Peypouquet: Convex Analysis in Normed Spaces: Theory, Methods and Examples, 2015.