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

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