非线性互补函数及其在不确定规划中的应用

Nonlinear Complementarity Function and Its Application in Uncertain Programming

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.