一类不可微多目标规划的Mond-Weir型对偶  

Mond-Weir Duality for a Class of Nondifferentiable Multiobjective Programming

作　　者：赵洁[1] 

机构地区：[1]重庆师范大学涉外商贸学院数学与计算机学院,重庆401520

出　　处：《重庆师范大学学报（自然科学版）》2017年第3期1-5,共5页Journal of Chongqing Normal University:Natural Science

基　　金：重庆师范大学涉外商贸学院"中青年骨干教师培养计划"

摘　　要：【目的】研究了一类不可微的多目标规划问题,其中目标函数包含支撑函数,约束包含等式和不等式。【方法】给出了该问题的一类Mond-Weir型对偶模型,利用G-KKT最优性必要条件和G-不变凸性证明了原问题与对偶问题的对偶结果。【结果】在适当条件下,得到该问题与对偶问题的弱对偶定理、强对偶定理、逆对偶定理和非极大逆对偶定理,并进行了证明。【结论】将相关结论推广到了非可微情形。[Purposes] Mond-Weir type dual problem of a class of nondifferentiable multiobjective programs were studied, the problems with both inequality and equality constrains in which every component of the objective function contains a term involving the support function of a compact convex set were considered. [Methods] Mode-Weir type dual problem was formulated. G-KKT necessary optimality conditions and G invex assumption were used to establish duality theorems relating the problem and the dual problems. [Findings]Weak duality theorems, strong duality theorem, converse duality theorem and no maximal converse duality theorem were established under suitable conditions. [Conclusions]The work generalized some related results to the nondifferentiable

关 键 词：不可微规划 多目标规划 MOND-WEIR型对偶 G-不变凸 

分 类 号：O221.6[理学—运筹学与控制论]