Higher Order Duality of Multiobjective Constrained Ratio Optimization Problems

Abstract

In this article, a constrained nondifferentiable multiobjective fractional programming problem is considered.
A new concept in generalized convexity, called higher order $\, (C, \alpha, \gamma,\rho,d)\,$ 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 $\, (C, \alpha, \gamma,\rho,d)\,$ type-I functions and not in the class of $\; (C, \alpha, \rho,d)\;$ type-I functions already existing in the literature. Based upon the higher order $\; (C, \alpha, \gamma,\rho,d)\;$ 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.