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

@inproceedings{Fazell2004LogdetHF,
  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},
  year={2004}
}
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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References

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Showing 1-10 of 17 references

Matrix Rank Minimization with Applications

M. Fazel
PhD thesis, Dept. of Elec. Eng., Stanford University • 2002
View 3 Excerpts
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volume 6

M. Fazel, H. Hindi, S. P. Boyd. A rank minimization heuristic with applic Conference
pages 4734–4739, June • 2001
View 2 Excerpts

17(1):11–22

M. W. Trosset. Distance matrix completion by numerica Optimization, Applications
October • 2000

Modern Multidimensional Scaling: Theory and Applications

I. Borg, P. Groenen
Springer • 1997

38(1):49–95

L. Vandenberghe, S. Boyd. Semidefinite programming. SIAM Review
March • 1996

In Proceedings of IFAC 96

E. Beran, K. Grigoriadis. A combined alternating projection, semidefinite programming algorithm for low-order control design
volume C, pages 85–90, July • 1996

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