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Disk matrices and the proximal mapping for the numerical radius

X.Y. Han(xh332***at***cornell.edu)
Adrian Lewis(adrian.lewis***at***cornell.edu)

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.

Keywords: field of values, numerical radius, proximal mapping, partial smoothness, semidefinite program

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: ORIE Cornell, April 2020

Download: [PDF]

Entry Submitted: 04/29/2020
Entry Accepted: 04/29/2020
Entry Last Modified: 04/29/2020

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