Inequality Systems and Global OptimizationU

Solvability results for infinite inequality systems involving convex and difference of convex DC. functions are given. Generalizations of Farkas’ lemma are obtained. These results are presented in terms of epigraphs of conjugate functions. Applications are given for characterizing global e-optimality and optimality.of difference of convex DC. optimization problems with convex inequality constraints. Solvability results for cone convex inequality systems are also given.