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

@article{Recht2010GuaranteedMS,
  title={Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization},
  author={B. Recht and M. Fazel and P. Parrilo},
  journal={SIAM Review},
  year={2010},
  volume={52},
  pages={471-501}
}
  • B. Recht, M. Fazel, P. Parrilo
  • Published 2010
  • Mathematics, Computer Science
  • SIAM Review
  • 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… CONTINUE READING
    Null space conditions and thresholds for rank minimization
    134
    Guaranteed Rank Minimization via Singular Value Projection
    431
    A fast and efficient heuristic nuclear-norm algorithm for affine rank minimization
    8
    An Accelerated Proximal Gradient Algorithm for Nuclear Norm Regularized Least Squares Problems
    303
    A FAST AND EFFICIENT HEURISTIC NUCLEAR-NORM ALGORITHM FOR AFFINE RANKMINIMIZATION
    Affine matrix rank minimization problem via non-convex fraction function penalty
    13
    Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization
    126

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 112 REFERENCES
    Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
    408
    Sparse nonnegative solution of underdetermined linear equations by linear programming.
    546
    Distance Matrix Completion by Numerical Optimization
    50
    A rank minimization heuristic with application to minimum order system approximation
    879
    Local Minima and Convergence in Low-Rank Semidefinite Programming
    274
    Structured low-rank approximation and its applications
    183
    On cone-invariant linear matrix inequalities
    28