Farkas-Type Results and Duality for DC Programs with Convex Constraints

We are interested in new versions of Farkas lemmas for systems involving convex and DC-inequalities. These versions extend well-known Farkas-type results published recently, which were used as main tools in the study of convex optimization problems. The results are used to derive several strong duality results such as: Lagrange, Fenchel-Lagrange or Toland-Fenchel-Lagrange duality for DC and convex problems. Moreover, it is shown that for this class of problems, these versions of Farkas lemma are actually equivalent to several strong duality results of Lagrange, Fenchel-Lagrange or Toland-Fenchel-Lagrange types.