B-预不变凸函数在多目标规划中的对偶问题

B-预不变凸函数是一类十分重要的广义凸性函数,是对B-凸函数的一种十分重要的推广形式。自S.K.Suneja等人建立B-预不变凸函数的概念以来,许多学者对其进行了更加深入的研究,得出了一系列十分重要的结果。本文基于广义凸性在数学规划及最优化理论中的重要作用,在已有文献的基础上,利用函数的B-预不变凸性,给出了多目标规划的一些对偶性结果,分别建立了Mond-Weir型对偶模型和Wolf型对偶模型的强对偶性和弱对偶性结果,本文的结论是对最近一些文献中相应结论的改进与推广。

Duality of Multi-objective Programming about B-preinvex Function

B-preinvex function is a kind of important generalized convex functions.It is an important generalization for B-convex function.Since the concept of B-preinvex function is introduced by S.K.Suneja etc,many scholars investigated its characterizations and applications in mathematical programming and optimization theory more thoroughly.A series of important conclusions has been obtained. Based on the important effect of generalized convexity in mathematical programming and optimization theory and under the existed results,some duality results about multi-objective programming are obtained under differentiable B-preinvex function in this paper.The sufficient conditions of weak efficient solution are given.Some conclusions about strong duality and weak duality for Mond-Weir type model and Wolf type model are constructed.These conclusions are generalizations of corresponding results.