All convex bodies in the subdifferential of a locally Lipschitz function.

Abstract: We construct a differentiable locally Lipschitz function f in R^d with the following property: for every convex body K of R^d, there exists x in R^d such that the subdifferential of f at x coincides with K (in the sense of limiting or Clarke).

We show that our technique can be further refined to recover all compact connected subsets with nonempty interior in the image of the limiting subdifferential of a locally Lipschitz function.
We end this talk with a brief discussion about how large the set of functions with the aforementioned property is.

Posted on Jun 24, 2024 in Optimization and Equilibrium, Seminars