求解随机广义互补问题的期望残差最小化方法

Expected Residual Minimization Method for Stochastic Generalized Complementary Problems

由于广义互补问题有着广泛的应用,并且在实际应用中存在很多不确定因素。因此,本文主要考虑随机广义互补问题。通过所谓的NCP函数给出它的期望残差最小化(ERM)模型。由于所给出的ERM模型中含有一个积分计算。一般情况下,积分计算很难得到精确值。因此,本文引入拟蒙特卡罗方法,并用此方法给出ERM问题的近似问题。进一步,证明了在一定条件下,由ERM问题的近似问题得到的解的序列收敛到ERM问题的解。

In practice, generalized complementary problems have many applications and many elements may involve uncertain data in applications. Therefore, we mainly consider the stochastic generalized complementary problems. We employ the so called NCP function to give the expected residual minimization (ERM) model. Since the ERM formulation includes an integration, which is generally difficult to evaluate exactly, we propose the quasi-Monte Carlo method to give an approximation problem for ERM formulation. Furthermore, we show that the solutions of this approximation problem converge to the solution of the ERM formulation under very mild conditions.