Disk matrices and the proximal mapping for the numerical radius
Optimization and Control
2020-05-01 v1
Abstract
Optimal matrices for problems involving the matrix numerical radius often have fields of values that are disks, a phenomenon associated with partial smoothness. Such matrices are highly structured: we experiment in particular with the proximal mapping for the radius, which often maps n-by-n random matrix inputs into a particular manifold of disk matrices that has real codimension 2n. The outputs, computed via semidefinite programming, also satisfy an unusual rank property at optimality.
Cite
@article{arxiv.2004.14542,
title = {Disk matrices and the proximal mapping for the numerical radius},
author = {X. Y. Han and Adrian S. Lewis},
journal= {arXiv preprint arXiv:2004.14542},
year = {2020}
}
Comments
18 pages, 2 figures