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Optimization Letters

, Volume 6, Issue 5, pp 841–849 | Cite as

Convexifying the set of matrices of bounded rank: applications to the quasiconvexification and convexification of the rank function

  • Jean-Baptiste Hiriart-Urruty
  • Hai Yen LeEmail author
Original Paper

Abstract

We provide an explicit description of the convex hull of the set of matrices of bounded rank, restricted to balls for the spectral norm. As applications, we deduce two relaxed forms of the rank function restricted to balls for the spectral norm: one is the quasiconvex hull of this rank function, another one is the convex hull of the rank function, thus retrieving Fazel’s theorem (Matrix rank minimization with applications, 2002).

Keywords

Rank of a matrix Spectral norm Trace (or nuclear) norm Quasiconvex hull of a function 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut de mathématiques de ToulouseUniversité Paul Sabatier (Toulouse III)Toulouse Cedex 09France

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