Fully copositive matrices

The class of fully copositive (C-0(f)) 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 Q(0)-matrices are P-0-matrices. As a corollary of this main result, we establish that a bisymmetric Q(0)-matrix is positive semidefinite if, and only if, it is fully copositive. Another important result of the paper is a constructive characterization of Q(0)-matrices within the class of C-0(f). 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 C-0(f) boolean AND Q(0) class. As a byproduct of this characterization, we observe that a C-0(f)-matrix is in Q(0) if, and only if, it is completely Q(0). 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 C-0(f) boolean AND Q(0) class can be processed by Lemke's algorithm. (C) 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.