Expected residual minimization method for stochastic linear complementarity problems
Expected residual minimization method for stochastic linear complementarity problems
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DOI：
10.1287/moor.1050.0160
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发表时间：
2005-11-01
影响因子：
1.7
通讯作者：
Fukushima, M
中科院分区：
文献类型：
--
作者：
Chen, XJ;Fukushima, M
本文提出了一种新的随机线性互补问题（SLCP），其目标是极小化由NCP函数定义的期望残差。我们通过拟蒙特卡罗方法生成观测值，证明了离散逼近问题极小值的每一个聚点都是SLCP的最小期望剩余解。我们证明了期望残差最小化（ERM）问题及其离散近似解存在的充分条件是存在一个观测值Ω（1）使得系数矩阵M（Ω（1））是R1矩阵.此外，我们表明，对于一类问题与固定系数矩阵，ERM问题成为连续可微的，可以解决，而不使用离散逼近。炼油厂生产问题的初步数值结果表明，新配方的解决方案是可取的。
This paper presents a new formulation for the stochastic linear complementarity problem (SLCP), which aims at minimizing an expected residual defined by an NCP function. We generate observations by the quasi-Monte Carlo methods and prove that every accumulation point of minimizers of discrete approximation problems is a minimum expected residual solution of the SLCP. We show that a sufficient condition for the existence of a solution to the expected residual minimization (ERM) problem and its discrete approximations is that there is an observation omega(1) such that the coefficient matrix M(omega(1)) is an R, matrix. Furthermore, we show that, for a class of problems with fixed coefficient matrices, the ERM problem becomes continuously differentiable and can be solved without using discrete approximation. Preliminary numerical results on a refinery production problem indicate that a solution of the new formulation is desirable.