Orthogonal invariance and identifiability

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

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)580-598
JournalSIAM Journal on Matrix Analysis and Applications
Volume35
Issue number2
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Duality
  • Eigenvalues
  • Identifiable set
  • Partial smoothness
  • Polyhedra
  • Symmetric matrix

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