OPTIMALITY AND DUALITY FOR MULTIOBJECTIVE FRACTIONAL PROGRAMMING PROBLEMS WITH n-SET FUNCTIONS AND GENERALIZED V -TYPE-I UNIVEXITY

Problems of multiobjective optimization are widespread in mathematical modelling of real world systems for a very broad range of applications. In particular, several classes of multiobjective problems with set and n-set functions have been the subject of several papers in the last few decades. For a historical survey of optimality conditions and duality for programming problems involving set and n-set functions the reader is referred to Stancu-Minasian and Preda’s review paper [8]. General theory for optimizing n-set functions was first developed by Morris [5] who, for fractions of a single set, obtained results that are similar to the standard mathematical programming problem. Corley [1] gave the concept of derivative of a real-valued n-set function and generalized the results of Morris [5] to n-set functions and established optimality conditions and Lagrangian duality. Along the lines of Jeyakumar and Mond [3], and Mishra et al. [4], Preda et al. [6] defined new classes of n-set functions, called (ρ, ρ′)-V -univex typeI, (ρ, ρ′)-quasi-V -univex type-I, (ρ, ρ′)-pseudo-V -univex type-I, (ρ, ρ′)-quasi pseudo-V -univex type-I and (ρ, ρ′)-pseudo quasi-V -univex type-I. They obtained necessary and sufficient optimality criteria and some duality results.