The Lyapunov rank of a cone is the number of independent equations obtainable from an analogue of the complementary slackness condition in cone programming problems, and more equations are generally thought to be better. Bounding the Lyapunov rank of a proper cone in R^n from above is an open problem. Gowda and Tao gave an … Read more
If K is a closed convex cone and if L is a linear operator having L(K) a subset of K, then L is a positive operator on K and L preserves inequality with respect to K. The set of all positive operators on K is denoted by pi(K). If J is the dual of K, … Read more
A real square matrix Q is a bilinear complementarity relation on a proper cone K in R^n if x in K, s in K^* with x perpendicular to s implies x^{T}Qs=0, where K^* is the dual of K. The bilinearity rank of K is the dimension of the space of all bilinear complementarity relations on … Read more