Robust solution of monotone stochastic linear complementarity problems
Robust solution of monotone stochastic linear complementarity problems
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DOI：
10.1007/s10107-007-0163-z
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发表时间：
2009-03-01
影响因子：
2.7
通讯作者：
Fukushima, Masao
中科院分区：
文献类型：
--
作者：
Chen, Xiaojun;Zhang, Chao;Fukushima, Masao
我们考虑涉及期望矩阵为正半定的随机矩阵的随机线性互补问题（SLCP）。我们证明，如果使用正半定期望矩阵简化为 LCP 的期望值 (EV) 公式具有非空且有界的解集，则该问题的期望残差最小化 (ERM) 公式具有非空且有界的解集。我们为单调 LCP 给出了一个新的误差界，并用它来表明 ERM 公式的解是稳健的，因为它们对于 SLCP 中的随机参数变化可能具有最小的敏感性。给出了包括随机交通均衡问题在内的数值例子来说明解的特征。
We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semi-definite. We show that the expected residual minimization (ERM) formulation of this problem has a nonempty and bounded solution set if the expected value (EV) formulation, which reduces to the LCP with the positive semi-definite expectation matrix, has a nonempty and bounded solution set. We give a new error bound for the monotone LCP and use it to show that solutions of the ERM formulation are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in SLCP. Numerical examples including a stochastic traffic equilibrium problem are given to illustrate the characteristics of the solutions.