In this paper we consider the classical problem of finding a low rank approximation of a given matrix. In a least squares sense a closed form solution is available via factorization. However, with additional constraints, or in the presence of missing data, the problem becomes much more difficult. In this paper we show how to efficiently compute the convex envelopes of a class of rank minimization formulations. This opens up the possibility of adding additional convex constraints and functions to the minimization problem resulting in strong convex relaxations. We evaluate the framework on both real and synthetic data sets and demonstrate state-of-the-art performance.


Singular Value Decomposition Trust Region Measurement Matrix Convex Relaxation Convex Envelope 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Viktor Larsson
    • 1
  • Carl Olsson
    • 1
  1. 1.Centre for Mathematical SciencesLund UniversitySweden

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