Effciency Conditions And Duality For A Class Of Multiobjective Fractional Programming Problems

An important method for the theory research of the multi-objective optimization problem (MOPS) is to find out the sufficient conditions for a certain class of (MOPS) under the different convexity hypothesizes, establish duality for original problems and explore the relation between the solutions of the original and the duality problems. In recent years, many authors have been studying the multi-objective fractional programming problems (MFPS) under the assumption of all kinds of generalized convexity. Many efficiency conditions and duality theorems of (MFPS) have been given based on the concepts of all kinds of generalized convexity. In this paper, we firstly review some basic concepts about the generalized convexity of function andpresent a unified formulation of generalized convexity, (F,α,ρ,d)- convexity.Under the assumption of (F,α,ρ,d)- convexity of the objective function andconstraint functions, the efficiency conditions for (MFPS) are showed. Two types of duality to (MFPS) are introduced by means of Lagrangian. A weak duality theorem and a strong duality theorem are proved for each type of duality respectively based onthe (F,a, p, d) - convexity.