A Class Of Nondifferentiable Multiobjective Generalized Fractional Mathematical Programming Problems

For a class of nondifferentiable and noncovex multiobjective generalized fractional mathematical programming problem (VFP), whose subobjective functions are generalized fractions and including restrictions of abstract inequality and anstract set, Kuhn-Tucker type optimality conditions, saddle-point type optimal-ity conditions, Lagrange duality and the criterion of esistence of exat penalty function of a special case of (VFP) are concerned. The paper consists of 4 chapters.In chapter 1, we state the recent advances in the study of multobjective fractional and single-objective generalized fractional programming. Then the work we do on this problem is introduced.Chapter 2 is the main part of the paper. In section 1, some definitions and notations are introduced, and several preliminary results are proposed. In section 2, under the proper constraint qualifications, we develop the Kuhn-Tucker type necessary conditions for weak efficiency and proper efficiency of problem (VFP) with the help of convex analysis, the definition of the Clarke's generalized directional derivative and generalized gradient. In section 3, under the assumptions of generalized ρ—convexity, we present the Kuhn-Tucker type sufficient conditions in which the weak efficiency, efficiency and proper efficiency are involved.In chapter 3; under the assumptions of subconvexlike and generalized sub-convexlike, we propose the saddle point type optimality conditions and Lagrange...