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SIAMREV
2010

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

8 years 1 months ago
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard, because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability, provided the codimension of the subspace is sufficiently large. The...
Benjamin Recht, Maryam Fazel, Pablo A. Parrilo
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMREV
Authors Benjamin Recht, Maryam Fazel, Pablo A. Parrilo
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