G-b-(p,r,?)-optimality And Duality Of Invex Multiobjective Programming

In this paper,a new class of generalized invex functions were defined by using Clark generalized gradient on the basis of G-invex functions and B-invex functions.There were G-B-(p,r,?)-invex functions,G-B-(p,r,?)-pseudo invex functions,GB-(p,r,?)-quasi invex functions,The optimality Mond-Weir type duality and Wolfe type duality of multi-objective programming problems and multi-objective fractional programming problems were discussed.And then,several optimality conditions,weak duality,strong duality,strict inverse duality theorem were obtained.The mainly work that we did were as follows:(1)The basic concept of G-B-(p,r,?)-invex function were defined,and the the concept of G-B-(p,r,?)-pseudo invex function and G-B-(p,r,?)-quasi invex function were given.(2)On the basis of the newly defined functions,the optimality of multi-objective were discussed.Then,the model of Mond-Weir type and Wofe type programming were established.And the several optimality sufficiencies condition,the weak dual theorem,strong dual theorem and strict inverse duality theorem of corresponding programming were obtained.(3)The optimality conditions of multi-objective fractional programming problems limited by generalized G-B-(p,r,?)-invex functions were discussed.At the same time,the Mond-Weir type programming and Wolfe type programming were estabLished.And then several optimality theorems,weak dual theorems,strong dual theorEms,strict inverse dual theorems were obtained.