互补约束数学规划问题的对偶性  

Duality in Mathematical Programs with Complementarity Constraints

作　　者：赵晶 李沛瑜 ZHAO Jing;LI Peiyu(Information and Educational Technology Center,Zhejiang University City Collage,Hangzhou Zhejiang 310015;School of Mathematics.Southwest Minzu University,Chengdu Sichuan 610225,China)

机构地区：[1]浙大城市学院信息与教育技术中心,杭州310015 [2]西南民族大学数学学院,成都610225

出　　处：《重庆师范大学学报（自然科学版）》2021年第6期9-14,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11501476);西南民族大学引进人才科研启动项目(No.RQD2021065)。

摘　　要：【目的】研究互补约束数学规划问题的Mond-Weir型对偶。【方法】把非线性规划问题的Mond-Weir型对偶推广到互补约束数学规划问题。【结果】在一些弱凸性条件下证明了弱对偶定理、强对偶定理和严格逆对偶定理。【结论】举例说明本文给出的互补约束数学规划问题Mond-Weir型对偶是合理的。[Purposes]Study the Mond-Weir type duality in mathematical programs with complementarity constraints.[Methods]Generalize the Mond-Weir type duality in nonlinear programming problem to mathematical programs with complementarity constraints.[Findings]Under some mild conditions,establish the weak duality theorem,the strong duality theorem and the strict converse duality theorem.[Conclusions]Give some examples to show that the Mond-Weir type duality in mathematical programs with complementarity constraints is reasonable.

关 键 词：互补约束数学规划问题 MOND-WEIR对偶 弱对偶 强对偶 严格逆对偶 

分 类 号：O221[理学—运筹学与控制论]