A collection of nonsmooth Riemannian optimization problems

Abstract

Nonsmooth Riemannian optimization is a still scarcely explored subfield of optimization theory that concerns the general problem of minimizing (or maximizing), over a domain endowed with a manifold structure, a real-valued function that is not everywhere differentiable. The purpose of this paper is to illustrate, by means of nine concrete examples, that nonsmooth Riemannian optimization finds numerous applications in engineering and the sciences.