This article studies a pair of higher order nondifferentiable symmetric fractional programming problem over cones. First, cone convex function is introduced. Then using the properties this function, duality results are set up, which give legitimacy primal dual model.

In this paper, a generalization of convexity, namely Gf-invexity is considered. We formulate Mond-Weir type symmetric dual for class nondifferentiable multiobjective fractional programming problem over cones. Next, we prove appropriate duality results using assumptions.

Consider a proper cone K ⊂ < and its dual cone K. It is well known that the complementary slackness condition xs = 0 defines an n-dimensional manifold C(K) = { (x, s) : x ∈ K, s ∈ K, xs = 0 } ⊂ <×<. When K is a symmetric cone, this manifold can be described by a set of n bilinear equalities. This fact proves to be very useful when optimizing over such cones, therefore it is natural to look for ...

For a proper cone K ⊂ Rn and its dual cone K∗ the complementary slackness condition xT s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K∗ }. When K is a symmetric cone, this fact translates to a set of n linearly independent bilinear identities (optimality conditions) satisfied by every (x, s) ∈ C(K). This proves to be very useful when optimizing over such cones,...