Techniques of variational analysis

Variational arguments can be traced back to the early development of the calculus of variations. The discovery of modern variational principles and nonsmooth analysis further expand the range of applications of these techniques.

The lecture is an introduction to (mostly infinite-dimensional) first-order variational analysis, which includes several variational principles (Ekeland, Borwein-Preiss, DGZ, Stegall), subdifferential calculus, rudiments of convex analysis (convex subgradient, Fenchel duality theory, maximal monotone operators), and, as the peak of the lecture, nonsmooth analysis on smooth (finitely dimensional) Riemannian manifolds and its applications to spectral functions.

Our intention is to accommodate a broader audience, long and technical proofs will therefore be omitted. Various examples, applications, and open problems make the lecture more lively.

An elementary knowledge of functional analysis is the only prerequisite we anticipate.

The main reference for this lecture is the monograph "Techniques of variational analysis" by Borwein and Zhu.

Date and time info
Thursday, 10:15 - 11:45 h