Duality for εε-variational inequalities via the subdifferential calculus

Based on the properties of the (convex) εε-subdifferential calculus, we introduce to a general εε-variational inequality (formulated with the help of a set valued operator and a perturbation function) a dual one, expressed by making use of the (Fenchel) conjugate of the perturbation function. Under convexity hypotheses, we show that the fulfillment of a regularity condition guarantees that the primal εε-variational inequality is solvable if and only if its dual one is solvable. By particularizing the perturbation function, we obtain several dual statements and we succeed to generalize and improve a duality scheme recently given by Kum, Kim and Lee. An example justifying this generalization is also provided. Among the special instances of the general result, we rediscover also the duality scheme concerning variational inequalities due to Mosco.