Smoothing by mollifiers. Part Ⅱ: nonlinear optimization

摘要

This article complements the paper (Jongen, Stein, Smoothing by mollifers part I: semi-infinite optimization J Glob Optim doi: 10.1007/s 10898-007-9232-3), 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.