Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization
Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization
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DOI：
10.1007/s10107-007-0119-3
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发表时间：
2008-06
影响因子：
2.7
通讯作者：
G. Lin;Xiaojun Chen;M. Fukushima
中科院分区：
文献类型：
--
作者：
G. Lin;Xiaojun Chen;M. Fukushima
本文研究了带线性互补约束的随机数学规划问题，包括两类模型：此时此刻问题和低层观望问题。对于有限样本空间的问题，我们提出了一种光滑隐式规划与罚函数相结合的方法。然后，我们提出了一个解决连续随机变量问题的拟蒙特卡罗近似方法。一个全面的收敛理论也包括在内。我们进一步报告的数值结果与所谓的野餐供应商决策问题。
In this paper, we consider the stochastic mathematical programs with linear complementarity constraints, which include two kinds of models called here-and-now and lower-level wait-and-see problems. We present a combined smoothing implicit programming and penalty method for the problems with a finite sample space. Then, we suggest a quasi-Monte Carlo approximation method for solving a problem with continuous random variables. A comprehensive convergence theory is included as well. We further report numerical results with the so-called picnic vender decision problem.