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.
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