Binary positive semidefinite matrices and associated integer polytopes
نویسندگان
چکیده
منابع مشابه
Binary Positive Semidefinite Matrices and Associated Integer Polytopes
We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and well-known integer polytopes — the cut, boolean quadric, multicut and clique partitioning polytopes — are shown to arise as projections of binary psd polyt...
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In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].
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The positive semidefinite (psd) rank of a polytope is the smallest k for which the cone of k × k real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals this lower bound.
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in this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl. 308 (2000) 203-211] and [linear algebra appl. 428 (2008) 2177-2191].
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We build upon the work of Fukuda et al. [SIAM J. Optim., 11 (2001), pp. 647–674] and Nakata et al. [Math. Program., 95 (2003), pp. 303–327], in which the theory of partial positive semidefinite matrices was applied to the semidefinite programming (SDP) problem as a technique for exploiting sparsity in the data. In contrast to their work, which improved an existing algorithm based on a standard ...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2010
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-010-0352-z