摘要: 本文引入不确定线性互补问题鲁棒解的概念。而且,我们证明:如果不确定二次规划问题的robust Counterpart,这一鲁棒优化问题的存在最优解
![](https://image.hanspub.org/IMAGE/Edit_ccc41292-76ab-4c8c-890d-d74e6d57f550.jpg)
,并且最优值为0,那么
![](https://image.hanspub.org/IMAGE/Edit_82633981-ec02-422a-ae23-82d71e54a276.jpg)
就是不确定线性互补问题的鲁棒解。我们讨论当不确定集为随机对称分布时,线性互补问题的求解。借助于概率论知识,给出
![](https://image.hanspub.org/IMAGE/Edit_af81999f-81d3-4482-8caa-6afff168920c.jpg)
为almost reliable鲁棒解的充要条件。
Abstract:
In this paper, we introduce the notion of robust solution of uncertain linear complementarity problems. We prove that, if robust counterpart to uncertain quadratic programming—a robust optimization problem, has a optimal solution
![](https://image.hanspub.org/IMAGE/Edit_7e11ab6e-759f-4975-bdd6-5d2d0f9ad962.jpg)
, and the optimum value equals to zero, then
![](https://image.hanspub.org/IMAGE/Edit_c2a7c73e-6d6b-49fe-8ab1-55f4daf630f3.jpg)
is the robust solution of the uncertain linear complementarity problem. By probability theory, we discuss linear complementarity problems under a random symmetric uncertainty, and obtain sufficient and necessary conditions of almost reliable robust solution.