A collection of nonsmooth Riemannian optimization problems (Q2319933)

This paper is a plea for nonsmooth Riemannian optimization, a direction in optimization theory where real-valued functions that are not everywhere differentiable are minimized (respectively maximized) over domains endowed with a manifold structure. The authors present nine different problems (sparse principal component analysis, dimensionality reduction, economic load dispatch, independent component analysis, sphere packing on manifolds, low-rank matrix completion, sparsest vector identification, restoring manifold-valued images and oriented bounding box) that belong to this research area and motivate thus the need for more investigations in this direction. For the entire collection see [Zbl 1417.49001].