  In the second part of our study we introduce the concept of global extended
exactness of penalty and augmented Lagrangian functions, and derive the
localization principle in the extended form. The main idea behind the extended
exactness consists in an extension of the original constrained optimization
problem by adding some extra variables, and then construction of a
penalty/augmented Lagrangian function for the extended problem. This approach
allows one to design extended penalty/augmented Lagrangian functions having
some useful properties (such as smoothness), which their counterparts for the
original problem might not possess. In turn, the global exactness of such
extended merit functions can be easily proved with the use of the localization
principle presented in this paper, which reduces the study of global exactness
to a local analysis of a merit function based on sufficient optimality
conditions and constraint qualifications. We utilize the localization principle
in order to obtain simple necessary and sufficient conditions for the global
exactness of the extended penalty function introduced by Huyer and Neumaier,
and in order to construct a globally exact continuously differentiable
augmented Lagrangian function for nonlinear semidefinite programming problems.
