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. [ABSTRACT FROM AUTHOR]