Ln this paper bearing the same title as our earlier survey-paper [11] we pu
rsue the goal of characterizing the global solutions of an optimization pro
blem, i.e. getting at necessary and sufficient conditions for a feasible po
int to be a global minimizer (or maximizer) of the objective function. We e
mphasize nonconvex optimization problems presenting some specific structure
s like 'convex-anticonvex' ones or quadratic ones.