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

Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

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A new concept in generalized convexity, called higher order (C, α, γ, ρ, d) type-I functions, is introduced. To show the existence of such type of functions, we identify a function lying exclusively in the class of higher order (C, α, γ, ρ, d) type-I functions and not in the class of (C, α, ρ, d) type-I functions already existing in the literature. Based upon the higher order (C, α, γ, ρ, d) type-I functions, the optimality conditions for a feasible solution to be an efficient solution are derived. A higher order Schaible dual has been then formulated for nondifferentiable multiobjective fractional programs. Weak, strong and strict converse duality theorems are established for higher order Schaible dual model and relevant proofs are given under the aforesaid function.2010 Mathematics Subject Classification. Primary 90C26 90C29, 90C30, 90C32, 90C46

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