  In this article, we present new general results on existence of augmented
Lagrange multipliers. We define a penalty function associated with an augmented
Lagrangian, and prove that, under a certain growth assumption on the augmenting
function, an augmented Lagrange multiplier exists if and only if this penalty
function is exact. We also develop a new general approach to the study of
augmented Lagrange multipliers called the localization principle. The
localization principle allows one to study the local behaviour of the augmented
Lagrangian near globally optimal solutions of the initial optimization problem
in order to prove the existence of augmented Lagrange multipliers.
