  This article develops a duality principle for a class of optimization
problems in $\mathbb{R}^n$. The results are obtained based on standard tools of
convex analysis and on a well known result of Toland for D.C. optimization.
Global sufficient optimality conditions are also presented as well as relations
between the critical points of the primal and dual formulations. Finally we
formally prove there is no duality gap between the primal and dual formulations
in a local extremal context.
