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The Euclidean distance degree of orthogonally invariant matrix varieties

Dmitriy Drusvyatskiy(ddrusv***at***uw.edu)
Hon-Leung Lee(hllee***at***uw.edu )
Giorgio Ottaviani(ottavian***at***math.unifi.it)
Rekha R. Thomas(rrthomas***at***uw.edu )

Abstract: The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Euclidean distance degree of an orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances.

Keywords: Euclidean distance degree, algebraic variety, singular values, orthogonal group

Category 1: Convex and Nonsmooth Optimization (Other )


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Entry Submitted: 02/23/2016
Entry Accepted: 02/23/2016
Entry Last Modified: 02/23/2016

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