abadie’s qualification condition

Inner Conditions for Error Bounds and Metric Subregulerity of Multifunctions

  • Dominique Azé
    • Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Nonlinear Optimization Tags , , , , ,

    We introduce a new class of sets, functions and multifunctions which is shown to be large and to enjoy some nice common properties with the convex setting. Error bounds for objects attached to this class are characterized in terms of inner conditions of Abadie’s type, that is conditions bearing on normal cones and coderivatives at … Read more

    A Characterization of the Lagrange-Karush-Kuhn-Tucker Property

  • Dominique Azé
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    In this note, we revisit the classical first order necessary condition in mathematical programming in infinite dimension. We show that existence of Lagrange-Karush-Kuhn-Tucker multipliers is equivalent to the existence of an error bound for the constraint set, and is also equivalent to a generalized Abadie’s qualification condition. These results extend widely previous one like by … Read more