On the classes of fully copositive and fully semimonotone matrices

Abstract In this paper we consider the class C 0 f of fully copositive and the class E 0 f of fully semimonotone matrices. We show that C 0 f matrices with positive diagonal entries are column sufficient. We settle a conjecture made by Murthy and Parthasarathy to the effect that a C 0 f ∩ Q 0 matrix is positive semidefinite by providing a counterexample. We finally consider E 0 f matrices introduced by Cottle and Stone (Math. Program. 27 (1983) 191–213) and partially address Stone's conjecture to the effect that E 0 f ∩ Q 0 ⊆ P 0 by showing that E 0 f ∩ D c matrices are P 0 , where D c is the Doverspike class of matrices.

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