Duality and Farkas-type results for DC fractional programming with DC constraints

The aim of this paper is to discuss the fractional programming problem ( P ) that an objective function is a ratio of two DC (difference of convex) functions with finitely many DC constraints. A type of dual problem is constructed and the duality assertions are obtained. By using the obtained duality assertions, some Farkas-type results which characterize the optimal value of the problem ( P ) are given. Some programming problems considered in recent literature are the special cases of the problem ( P ) .