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2016 | 4 | 1 | 296-304
Tytuł artykułu

Zero-one completely positive matrices and the A(R, S) classes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A matrix of the form A = BBT where B is nonnegative is called completely positive (CP). Berman and Xu (2005) investigated a subclass of CP-matrices, called f0, 1g-completely positive matrices. We introduce a related concept and show connections between the two notions. An important relation to the so-called cut cone is established. Some results are shown for f0, 1g-completely positive matrices with given graphs, and for {0,1}-completely positive matrices constructed from the classes of (0, 1)-matrices with fixed row and column sums.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
296-304
Opis fizyczny
Daty
otrzymano
2016-04-06
zaakceptowano
2016-05-23
online
2016-07-18
Twórcy
autor
  • Department of Mathematics, University of Oslo, Oslo, Norway
  • Department of Mathematics, University of Oslo, Oslo, Norway
Bibliografia
  • [1] A. Berman and N. Shaked-Monderer. Completely Positive Matrices. World Scientific Publishing Co. Pte Ltd., Singapore, 2003.
  • [2] A. Berman and C. Xu. {0,1} Completely positive matrices. Linear Algebra Appl., 399:35–51, Apr 2005.
  • [3] A. Berman and C. Xu. Uniform and minimal {0,1}-cp matrices. Linear and Multilinear Algebra, 55(5):439–456, Sep 2007.
  • [4] R. A. Brualdi. Combinatorial Matrix Classes, volume 13. Cambridge University Press, Cambridge, 2006.
  • [5] S. Bundfuss and M. Dür. An adaptive linear approximation algorithm for copositive programs. SIAM J. Optim., 20(1):30–53, 2008.
  • [6] S. Burer. On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Program., 120(2):479–495, Apr 2008.
  • [7] G. Dahl. A note on diagonally dominant matrices. Linear Algebra Appl., 317(1-3):217–224, Sep 2000.
  • [8] M. Deza and M. Laurent. Geometry of Cuts and Metrics. Springer, 1997.
  • [9] M. Dür. Copositive Programming - A Survey. In Moritz Diehl, Francois Glineur, Elias Jarlebring, and Wim Michiels, editors, Recent Advances in Optimization and its Applications in Engineering, number 1, pages 3–21. Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.
  • [10] A. V. Karzanov. Metrics and undirected cuts. Math. Program., 32(2):183–198, 1985.
  • [11] F. Laburthe, M. Deza, and M. Laurent. The Hilbert basis of the cut cone over the complete graph on six vertices. Technical report, 1995.
  • [12] OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences, https://oeis.org, 2016.
  • [13] J. Zhong. Binary ranks and binary factorizations of nonnegative integermatrices. Electronic J. Linear Algebra, 23(June):540– 552, 2012.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0024
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