On Calmness of the Argmin Mapping in Parametric Optimization Problems

Recently, Cánovas et. al. [1] presented an interesting result: the argmin mapping of a linear semi-in nite program under canonical perturbations is calm if and only if some associated linear semi-in nite 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.