Abstract:

This paper deals with some new Farkas lemmas for a class of constraint fractional optimization with DC functions(the difference of convex functions). Following the idea due to Dinkelbach, we first associate the fractional optimization with a DC optimization problem. Then, by using the epigraph technique of the conjugate function, we introduce some new regularity conditions and establish the duality between the DC optimization problem and its Fenchel-Lagrange dual problem. Finally, we obtain some new Farkas lemmas for the fractional optimization problem. Furthermore, we also show that the results obtained in this paper extend and improve the corresponding results in the literature.

Key words: Fractional optimization, Regularity conditions, Farkas lemmas