  In this article we present a new perspective on the smooth exact penalty
function proposed by Huyer and Neumaier that is becoming more and more popular
tool for solving constrained optimization problems. Our approach to Huyer and
Neumaier's exact penalty function allows one to apply previously unused tools
(namely, parametric optimization) to the study of the exactness of this
function. We give a new simple proof of the local exactness of Huyer and
Neumair's penalty function that significantly generalizes all similar results
existing in the literature. We also obtain new necessary and sufficient
conditions for the global exactness of this penalty function.
