摘要
本文在非线性互补问题中引入不确定变量,提出了不确定非线性互补问题.给出了三种有限制的不确定非线性互补函数,证明了它们之间的等价性,并将三种有限制的非线性互补函数转化为各自的期望残差最小化模型,对模型水平集的有界性和误差界进行了研究,提供了非线性互补函数在不确定规划中的应用最后,给出了数值算例,验证了本文方法的可行性.
In this paper,by introducing uncertain variables into nonlinear complementarity problems,we propose uncertain nonlinear complementarity problem.At the same time,three kinds of uncertain nonlinear complementary functions are given and the equivalence between them is further proved.Subsequently,the expected residual minimization model of the uncertain nonlinear complementarity problem is proposed.The three restricted nonlinear complementary functions are transformed into their corresponding expected residual minimization models.Further more,the boundedness and error bounds of the level set of the model are established.Finally,we give the application of nonlinear complementarity function in uncertain programming,and the feasibility of this method is verified by a numerical example.
作者
贾芝福
李存林
JIA ZHIFU;LI CUNLIN(School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Ningria Key Laboratory of intelligent information and Big Data Processing,Governance and Social Management Research Center of Northwest Ethnic Regions,North Minzu University,Yinchuan 750021,China)
出处
《应用数学学报》
CSCD
北大核心
2022年第6期806-820,共15页
Acta Mathematicae Applicatae Sinica
基金
家民委重点人文社会科学基地"西北民族地区政府治理与社会管理研究中心"(71161001)
国家社会科学基金一般项目“公共服务购买中的供应商评价模型研究”(20BZZ065)
江苏省研究生科研与实践创新计划项目(KYCX20_0170)资助.
关键词
非线性互补函数
水平集
误差界
不确定规划
nonlinear complementarity function
level set
error bounds
uncertain programming