Smoothing by mollifiers. Part I: semi-infinite optimization

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 KarushKuhn-Tucker points of the original and the smoothed problem, and between their associated Morse indices, to prove the connectedness of the so-called min-max digraph for semi-infinite problems.

• Type: Journal
• Year: 2008
• Where: JGO
• Authors: Hubertus Th. Jongen, Oliver Stein
• Keywords: Compact Feasible Set, JGO 2008, Optimal Value Function, Single Smooth Function