Michael Orlitzky

Positive and Z-operators on closed convex cones

  • Michael Orlitzky
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    Let K be a closed convex cone with dual K-star in a finite-dimensional real Hilbert space V. A positive operator on K is a linear operator L on V such that L(K) is a subset of K. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. We say that L is … Read more

    The Lyapunov rank of an improper cone

  • Michael Orlitzky
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming Tags , , , ,

    Let K be a closed convex cone with dual K^* in a finite-dimensional real inner-product space V. The complementarity set of K is C(K) = { (x, s) in K × K^* | = 0 }. We say that a linear transformation L : V -> V is Lyapunov-like on K if = 0 for all (x, … Read more