一类广义univex条件下的多目标规划

Multiobjective Programming Under a Class of Generalized Univexity

引入了一种新的广义不变凸函数,即d-ρηθ-univex函数,讨论了这一概念与d-不变凸函数、d-univex函数、d-ρηθ-不变凸函数之间的关系,并在d-ρηθ-univex条件下考察一类多目标规划问题(P).首先给出问题(P)的弱Pareto有效解存在的充分条件;进而得到问题(P)的Mond-Weir型对偶的弱对偶、强对偶和逆对偶结论以及问题(P)的广义Mond-Weir型对偶的弱对偶和强对偶论断.

This paper introduces a new class of generalized invex function called d-pηθ-univex function,and discusses the relationship among d-invex, d-univex, d-pηθ-invex, and d-pηθ-univex functions.Under d-pηθ-univexity assumption, one type of multiobjective programming problem （P） is considered.The sufficient optimality conditions for the existence of the weak Pareto efficient solution of the problem（P） are first established. The results on the weak, strong and converse duality of Mond-Weir typeduality, and the weak and strong duality assertions of the generalized Mond-Weir type duality of the problem （P） are then obtained.