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

Gui-Hua Lin (), Huifu Xu () and Masao Fukushima ()

Mathematical Methods of Operations Research, 2008, vol. 67, issue 3, 423-441

Abstract: 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. Copyright Springer-Verlag 2008

Keywords: Stochastic mathematical program with equilibrium constraints; Monte Carlo/quasi-Monte Carlo methods; Penalization; 90C30; 90C33; 90C15 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00186-007-0201-x

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