Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2005-015 (December 02, 2005)

Monte Carlo and Quasi-Monte Carlo Sampling Methods for a Class of Stochastic Mathematical Programs with Equilibrium Constraints
by Gui-Hua Lin, Huifu Xu and Masao Fukushima

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In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints introduced by Birbil et al. (2004). 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.