Orthogonal invariance and identifiability

A. Daniilidis; D. Drusvyatskiy; A. S. Lewis

doi:10.1137/130916710

Orthogonal invariance and identifiability

A. Daniilidis, D. Drusvyatskiy, A. S. Lewis

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

21 Citations (Scopus)

Abstract

Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of "identifiability," a notion central to many activeset- type optimization algorithms. © 2014 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	580-598
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	35
Issue number	2
DOIs	https://doi.org/10.1137/130916710
Publication status	Published - 1 Jan 2014

Keywords

Duality
Eigenvalues
Identifiable set
Partial smoothness
Polyhedra
Symmetric matrix

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AB - Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of "identifiability," a notion central to many activeset- type optimization algorithms. © 2014 Society for Industrial and Applied Mathematics.

KW - Duality

KW - Eigenvalues

KW - Identifiable set

KW - Partial smoothness

KW - Polyhedra

KW - Symmetric matrix

U2 - 10.1137/130916710

DO - 10.1137/130916710

M3 - Article

VL - 35

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EP - 598

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

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