On Calmness of the Argmin Mapping in Parametric Optimization Problems
Recently, Cnovas et al. 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 of optimization models, while the opposite direction may fail in the general case. In applications to special classes of problems, we apply a more recent result on the intersection of calm multifunctions.
parametric optimization problems calm multifunctions optimal value function optimal set mapping perturbed nonlinear programs convex semi-infinite programs 49j53 49k40 90c31 90c34