z-matrix

Some Strongly Polynomially Solvable Convex Quadratic Programs with Bounded Variables

  • Jong-Shi Pang
  • Shaoning Han
    • Categories Applications - OR and Management Sciences, Nonlinear Optimization, Quadratic Programming Tags , , ,

    This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mbox{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of the problem. Extension of the Hessian class is also discussed. Our research is motivated by a recent reference [7] wherein the … Read more

    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