Optimality Conditions And Duality For Multiobjective Programming Under Generalized Type I Functions

The paper expanded some generalized convexity based on the former general-ized convexities and gave several generalized vector invexity function conepts such as V-Is·εtype, (h,φ)-Iεtype, generalized uniform V-Is·εtype. At the same time, the optimality and duality involving these new generalized convexities of non-smoooth multiobjective programming are researched and a series of optimality con-ditions,ε-optimality conditions and duality theorems are obtained.Several generalized vector invexity functions such as V-Is·εtype,quasi V-Is·εtype,pseudo V-Is·εtype,quasipseudo V-Is·εtype and pseudoquasi V-Is·εtype are defined in terms of symmetric gradient for a class of nonsmooth multiobjective programming over the former generalized convexity. The optimality sufficient condi-tions and duality for multiobjective programming (VP) are discussed involving these new generalized convexity.Based on Ben-Tal's generalized algebraic operations, new classes of functions namelly (h,φ)-Iεtype,quasi (h,φ)-Iεtype and pseudo (h,φ)-Iεtype functions are defined for a multiobjective programming (MOP)h,φ.The sufficient optimality conditions and some duality results are obtained for a feasible solution to be a Pareto efficient solution in this problem. Then, the optimality conditions and duality are researched for multiobjective programming (MOP)h,φunder the assumption of two classes of generalized (h,φ)-convex functions.Several generalized uniform V-Is·εtype invex function concepts are given for the multiobjective programming (VP). Some optimality conditions, some weak du-ality,strong duality and converse duality theorems for multiobjective programming (VP) are obtained under these generalized uniform V-Is·εtype invexity state.