随机对称不确定集下的线性互补问题

Linear Complementarity Problems under a Random Symmetric Uncertainty

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 ，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。

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 , 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.