Fully copositive matrices

Murthy, G. S. R. ; Parthasarathy, T. (1998) Fully copositive matrices Mathematical Programming, 82 (3). pp. 401-411. ISSN 0025-5610

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Official URL: http://www.springerlink.com/index/l3254l62v3w3161t...

Related URL: http://dx.doi.org/10.1007/BF01580077

Abstract

The class of fully copositive (C0f) matrices introduced in [G.S.R. Murthy, T. Parthasarathy, SIAM Journal on Matrix Analysis and Applications 16 (4) (1995) 1268-1286] is a subclass of fully semimonotone matrices and contains the class of positive semidefinite matrices. It is shown that fully copositive matrices within the class of Q0-matrices are P0-matrices. As a corollary of this main result, we establish that a bisymmetric Q0-matrix is positive semidefinite if, and only if, it is fully copositive. Another important result of the paper is a constructive characterization of Q0-matrices within the class of C0f. While establishing this characterization, it will be shown that Graves's principal pivoting method of solving Linear Complementarity Problems (LCPs) with positive semidefinite matrices is also applicable to C0f ∩ Q0 class. As a byproduct of this characterization, we observe that a C0f-matrix is in Q0 if, and only if, it is completely Q0. Also, from Aganagic and Cottle's [M. Aganagic, R. W. Cottle, Mathematical Programming 37 (1987) 223-231] result, it is observed that LCPs arising from C0f ∩ Q0 class can be processed by Lemke's algorithm.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Linear Complementarity Problem; Incidence; Matrix Classes; Principal Pivoting
ID Code:90943
Deposited On:15 May 2012 09:57
Last Modified:15 May 2012 09:57

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