Positive Subdefinite Matrices, Generalized Monotonicity, and Linear Complementarity Problems

Abstract

Positive subdefinite matrices were introduced by Martos to characterize generalized convex quadratic functions. This concept is extended to nonsymmetric matrices. It leads to a study of pseudomonotone matrices and to new characterizations of generalized monotone affine maps. Finally, some properties of linear complementarity problems involving such maps are derived.