Optimality And Duality For Generalized Higher-order Invex Function In Multiobjective Programming

Multi-objective programming is an interdisciplinary subject of applied mathematics and decision science.Convex functions are the basis of finance,mathematical statistics,and optimization theory.In multi-objective programming problems,most of the results are limited by the convexity of the objective function and the constraint function.However,because convex functions have certain limitations,and a large number of functions are non-convex in the practical problems we faced,therefore,the generalization of the convex function,namely the generalized convex function,is a hot subject studied by many scholars.This paper introduces invex functions to further discuss related problems in multi-objective programming.The generalized convexity not only retains the excellent properties of convex functions,but also extends and develops convex functions.On the basis of previous work,this paper makes a variety of generalizations of convex functions,this paper presents a new class of generalized higher-order convexity concepts,and studies the conditions for optimality,duality conclusions,and saddle-point problems of multi-objective programming and multi-objective fractional programming in which both the objective function and the constraints are new generalized higher-order convex functions.The main contents are as follows:(1)Firstly,a new class of generalized higher-order(F,?)-invex functions is defined,and its correctness is verified through appropriate examples.Secondly,under the condition of the new general convexity assumption,the optimality of the multi-objective fractional programming is studied,and some optimality sufficient conditions and saddle point theory are obtained.(2)The Mond-Weir type and Wolfe type dual models corresponding to higher-order(F,?)-invex multi-objective fractional programming are constructed,and the corresponding weak dual,strong dual,and inverse dual theorems are obtained and proved respectively.(3)Under the generalized higher-order(F,?)-invexity assumption,the higher-order Mond-Weir type and higher-order Wolfe type symmetric dual models of multi-objective programming are further constructed,several corresponding dual results are obtained and proved.