不适定线性二层规划问题的一种新的激励模型  

A new coordination model for ill-posed bilevel programming problem

作　　者：贾世会[1,2] 王兴趣 JIA Shihui;WANG Xingqu(Schonnl of Mathematics and Statistic, Wuhan University of Science and Technology, Wuhan 430081, China;Hubei Province Key Laboratory of Systems Science in Matallurgical Process,Wuhan 430081, China)

机构地区：[1]武汉科技大学理学院,武汉430081 [2]冶金工业过程系统科学湖北省重点实验室,武汉430081

出　　处：《华中师范大学学报（自然科学版）》2022年第2期226-230,235,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11501233,61671338,51204127);湖北省冶金工业过程重点实验室项目(Y201704).

摘　　要：针对不适定线性二层规划问题,考虑将部分合作模型中参数合作度更改为变量激励份额,由上层决策者适当分配激励份额给下层决策者,从而使得下层决策者心甘情愿与其合作.首先给出对应的激励模型,并给出与之相对应的罚问题.然后,证明了解的存在性,并设计相应算法来获得原二层规划问题的最优解.最后,数值实验不仅验证了该方法的可行性,并且结果显示,该文激励模型的最优值要优于部分合作模型的结果.For ill-posed linear bilevel programming problem,how the leader motivate the follower to maximize its own profit is studied.Firstly,a coordination model is presented with its corresponding penalty problem given.Then,under some conditions,the result on the existence of a solution is established and an algorithm is developed to obtain a coordination solution to the original bilevel programming problem.Finally,numerical results show that the proposed method is feasible.

关 键 词：线性规划 不适定二层规划 激励模型 罚函数 部分合作模型 

分 类 号：O221[理学—运筹学与控制论]