norms

New characterizations of Hoffman constants for systems of linear constraints

  • Javier F. Peña
  • Juan C. Vera
  • Luis F. Zuluaga
    • Categories Convex Optimization, Polyhedra Tags , ,

    We give a characterization of the Hoffman constant of a system of linear constraints in $\R^n$ relative to a reference polyhedron $R\subseteq\R^n$. The reference polyhedron $R$ represents constraints that are easy to satisfy such as box constraints. In the special case $R = \R^n$, we obtain a novel characterization of the classical Hoffman constant. More … Read more

    An algorithm to compute the Hoffman constant of a system of linear constraints

  • Javier F. Peña
  • Juan C. Vera
  • Luis F. Zuluaga
    • Categories Convex Optimization, Polyhedra Tags , ,

    We propose a combinatorial algorithm to compute the Hoffman constant of a system of linear equations and inequalities. The algorithm is based on a characterization of the Hoffman constant as the largest of a finite canonical collection of easy-to-compute Hoffman constants. Our algorithm and characterization extend to the more general context where some of the … Read more