optimal set mapping

Lipschitz Stability for a Class of Parametric Optimization Problems with Polyhedral Feasible Set Mapping

  • Diethard Klatte
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    This paper is devoted to the Lipschitz analysis of the solution sets and optimal values for a class of parametric optimization problems involving a polyhedral feasible set mapping and a quadratic objective function with arametric linear part. Recall that a multifunction is said to be polyhedral if its graph is the union of finitely many polyhedral … Read more

    On Calmness of the Argmin Mapping in Parametric Optimization Problems

  • Diethard Klatte
  • Bernd Kummer
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Semi-infinite Programming Tags , , ,

    Recently, Canovas et. al. (2013) presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality system is calm. Using classical tools from parametric optimization, we show that the if-direction of this condition holds in a much more general framework … Read more