The Multi-objective Programming Problem Under A Class Of Convxe Functions

In this paper,a class of new convex functions were proposed on the basis of(F,?,?,d)-convex functions and G-convex functions under local Lipschitz function conditions.These were G-(F,?,?,d)-convex function,G-(F,?,?,d)-quasi convex function,G-(F,?,?,d)-pseudo-convex functi on and weakly strict G-(F,?,?,d)-pseudo convex functions.Under the convexity constraint,the multi-objective programming problem were studied and the sufficient optimality conditions were obtained.Wolfe type dual programming and Mond-Weir type dual programming with new defined convexity were discussed.Weak dual theorem,strong dual theorem and strict inverse dual theorem of corresponding programming were obtained.Finally,multi-objective fractional programming problem were researched by new defined functions,many sufficient optimality conditions were obtained.Wolfe type dual programming and Mond-Weir type dual programming with new defined convexity were discussed.Weak dual theorem,strong dual theorem and strict inverse dual theorem of corresponding programming were obtained.The first part,the concept of G-(F,?,?,d)-convex function,weakly strict G-(F,?,?,d)-pseudo convex function,G-(F,?,?,d)-pseudo convex function and G-(F,?,?,d)-quasi convex function were defined;The second part,under the new convexity constraint,the multi-objective programming problem were studied and the sufficient optimality conditions were obtained.Wolfe type dual programming and Mond-Weir type dual programming with new defined convexity were discussed.Weak dual theorem,strong dual theorem and strict inverse dual theorem of corresponding programming were obtained;In the third part,the multi-objective fractional programming were studied by using the newly defined convex function,and the optimality theorem of the programming were obtained.At the same time,Wolfe type dual programming and Mond-Weir type dual programming were established.And the corresponding weak dual theorems,strong dual theorems and strict inverse dual theorems were obtained.