Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices

  title={Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices},
  author={Maryam Fazell and Haitham A. Hindi and Stephen P. Boyd},
We present a heuristic for minimizing the rank of a positive semidefinite matrix over a convex set. We use the logarithm of the determinant as a smooth approximation for rank, and locally minimize this function to obtain a sequence of trace minimization problems. We then present a lemma that relates the rank of any general matrix to that of a corresponding positive semidefinite one. Using this, we readily extend the proposed heuristic to handle general matrices. We examine the vector case as a… CONTINUE READING
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