On the classes of fully copositive and fully semimonotone matrices

AbstractIn this paper we consider the class C0f of fully copositive and the class E0f of fully semimonotone matrices. We show that C0f matrices with positive diagonal entries are column sufficient. We settle a conjecture made by Murthy and Parthasarathy to the effect that a C0f∩Q0 matrix is positive semidefinite by providing a counterexample. We finally consider E0f matrices introduced by Cottle and Stone (Math. Program. 27 (1983) 191–213) and partially address Stone's conjecture to the effect that E0f∩Q0⊆P0 by showing that E0f∩Dc matrices are P0, where Dc is the Doverspike class of matrices