Global optimization conditions for certain nonconvex minimization problems

By means of suitable dual problems to the following global optimization problems: extremum{f(x): x M X}, wheref is a proper convex and lower-semicontinuous function andM a nonempty, arbitrary subset of a reflexive Banach spaceX, we derive necessary and sufficient optimality conditions for a global minimizer. The method is also applicable to other nonconvex problems and leads to at least necessary global optimality conditions.