Abstract. This article complements the paper H. Th. Jongen, O. Stein: Smoothing by mollifiers. Part I: Semi-infinite optimization, where we showed that a compact feasible set of a standard semi-infinite optimization problem can be approximated arbitrarily well by a level set of a single smooth function with certain regularity properties. In the special case of nonlinear programming this function is constructed as the mollification of the finite min-function which describes the feasible set.
In the present article we treat the correspondences between Karush-Kuhn-Tucker points of the original and the smoothed problem, and between their associated Morse indices.