Smooth exact penalty functions: a general approach

In the article, we present a new perspective on the method of smooth exact penalty functions that is becoming more and more popular tool for solving constrained optimization problems. In particular, our approach to smooth exact penalty functions allows one to apply previously unused tools (namely, parametric optimization) to the study of these functions. We give a new simple proof of local exactness of smooth penalty functions that significantly generalizes all similar results existing in the literature. We also provide new necessary and sufficient conditions for a smooth penalty function to be globally exact.