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
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.