Disk matrices and the proximal mapping for the numerical radius
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.14542
- arXiv:
- arXiv:2004.14542
- Bibcode:
- 2020arXiv200414542H
- Keywords:
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- Mathematics - Optimization and Control;
- 15A60;
- 49J52;
- 90C22
- E-Print:
- 18 pages, 2 figures