Scenario Generation for Stochastic Problems via the Sparse Grid Method
نویسندگان
چکیده
Efficient generation of scenarios is a central problem in evaluating the expected value of a random function in the stochastic optimization. We study the use of sparse grid scenario generation method for this purpose. We show that this method is uniformly convergent, hence, also epi-convergent. We numerically compare the performance of the sparse grid method with several Quasi Monte Carlo (QMC) methods and the Monte Carlo (MC) method for scenario generation. The numerical results show that the sparse grid method is very efficient if the integrand has sufficient differentiability. A basic implementation of the sparse grid method also achieves competitive performance in the piece-wise linear case when compared to several QMC methods. On our test problems the sparse grid method is consistently superior than the Monte Carlo method.
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Scenario generation for stochastic optimization problems via the sparse grid method
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