Optimality and duality results for a nondifferentiable multiobjective fractional programming problem

The purpose of this paper is to study a class of nondifferentiable multiobjective fractional programming problems in which every component of objective functions contains a term involving the support function of a compact convex set. For a differentiable function, we introduce the definition of higher-order (C,alpha,gamma.rho,d)-convex function. A nontrivial example is also constructed which is in this class but not (F,alpha,gamma.rho,d))-convex. Based on the (C,alpha,gamma.rho,d))-convexity, sufficient optimality conditions for an efficient solution of the nondifferentiable multiobjective fractional programming problem are established. Further, a higher-order Mond-Weir type dual is formulated for this problem and appropriate duality results are proved under higher-order (C,alpha,gamma.rho,d))-assumptions.