(G-V,ρ)不变凸多目标规划的对偶条件  

Duality Conditions of Nonsmooth Semi-Infinite Multi-Objective Fractional Programming

作　　者：李向有[1] 苗红梅[2] LI Xiangyou;MIAO Hongmei(College of Mathematics and Computer Science,Yan'an University;College of Physics and Electronic Information,Yan'an University,Yan'an Shaanxi 716000,China)

机构地区：[1]延安大学数学与计算机科学学院 [2]延安大学物理与电子信息学院,陕西延安716000

出　　处：《重庆师范大学学报（自然科学版）》2020年第1期81-85,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11961072);陕西省教育厅科研项目(No.17JK0860)。

摘　　要：【目的】用更广义的凸函数来研究多目标规划问题。【方法】利用局部Lipschitz函数,定义了一类新的(G-V,ρ)不变凸函数,研究了涉及新定义函数的非可微半无限多目标规划问题。【结果】得到了Mond-Weir对偶问题的弱对偶条件和严格逆对偶条件。【结论】在新的凸性下推广了非可微多目标规划问题的对偶条件。[Purposes]To study multi-objective programming problem with more generalized convex functions.[Methods]By local Lipschitz functions,a class of new(G-V,ρ)invex functions were defined,non-differentiable semi-infinite multi-objective programming problems involving the new defined functions were researched.[Findings]Weak dual conditions and strictly converse dual conditions of Mond-Weir dual problem were obtained.[Conclusions]Dual conditions of non-differentiable multi-objective programming problem were generalized under the new convexity.

关 键 词：(G-V ρ)函数 多目标 半无限 对偶 

分 类 号：O221.6[理学—运筹学与控制论] O224[理学—数学]