随机对称不确定集下的线性互补问题

Linear Complementarity Problems under a Random Symmetric Uncertainty

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 ,并且最优值为0,那么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 为almost reliable鲁棒解的充要条件。

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 , and the optimum value equals to zero, then 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.