Friday, 15:15 - 15:40 h, Room: MA 141

 

Sanjay Mehrotra
New results in scenario generation for stochastic optimization problems via the sparse grid method

Coauthors: Michael Chen, David Papp

 

Abstract:
We study the use of sparse grid methods for the scenario generation (or discretization) problem in stochastic optimization problems when the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function, the sequence of optimal solutions of the sparse grid approximations converges to the true optimal solution as the number of scenarios increases. The rate of convergence is also established. An improvement is presented for stochastic programs in the case when the uncertainty is described using a linear transformation of a product of univariate distributions, such as joint normal distributions. We numerically compare the performance of sparse grid methods with quasi-Monte Carlo and Monte Carlo scenario generation. The results show that the sparse grid method is very efficient if the integrand is sufficiently smooth, and that the method is potentially scalable to thousands of random variables.

 

Talk 1 of the invited session Fri.3.MA 141
"Scenario generation in stochastic programming" [...]
Cluster 22
"Stochastic optimization" [...]

 

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