Smoothing by mollifiers. Part I: semi-infinite optimization

Authors:
Hubertus Th. Jongen;Oliver Stein
Affiliations:
Department of Mathematics --- C, RWTH Aachen University, Aachen, Germany 52056;School of Economics and Business Engineering, University of Karlsruhe, Karlsruhe, Germany 76128
Venue:
Journal of Global Optimization
Year:
2008

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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-called min---max digraph for semi-infinite problems.