Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints

被引：18

作者：

Lin, Gui-Hua ^{[1
]}

Xu, Huifu ^{[2
]}

Fukushima, Masao ^{[3
]}

机构：

[1] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China

[2] Univ Southampton, Sch Math, Highfield Southamptom, England

[3] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Kyoto 6068501, Japan

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2008年 / 67卷 / 03期

关键词：

stochastic mathematical program with equilibrium constraints; Monte Carlo/quasi-Monte Carlo methods; penalization;

D O I：

10.1007/s00186-007-0201-x

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints introduced by Birbil et al. (Math Oper Res 31:739-760, 2006). Firstly, by means of a Monte Carlo method, we obtain a nonsmooth discrete approximation of the original problem. Then, we propose a smoothing method together with a penalty technique to get a standard nonlinear programming problem. Some convergence results are established. Moreover, since quasi-Monte Carlo methods are generally faster than Monte Carlo methods, we discuss a quasi-Monte Carlo sampling approach as well. Furthermore, we give an example in economics to illustrate the model and show some numerical results with this example.

引用

页码：423 / 441

页数：19