In this paper we establish necessary as well as
sufficient conditions for a given feasible point to be a global
minimizer of smooth minimization problems with mixed variables.
These problems, for instance, cover box constrained smooth minimization
problems and bivalent optimization problems. In particular, our
results provide necessary global optimality conditions for difference
convex minimization problems, whereas our sufficient conditions
give easily verifiable conditions for global optimality of various
classes of nonconvex minimization problems, including the class of
difference of convex and quadratic minimization problems. We
discuss numerical examples to illustrate the optimality
conditions