Smoothing by mollifiers. Part I: Semi-infinite optimization
Abstract. We show 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. This function is constructed as the mollification of the lower level optimal value function. Moreover, we use correspondences between Karush-Kuhn-Tucker points of the original and the smoothed problem, and between their associated Morse indices, to prove the connectedness of the so-call min-max digraph for semi-infinite problems.