Volume 2004
http://edoc.hu-berlin.de/18452/361
2022-09-28T12:19:58ZOn the Fortet-Mourier metric for the stability of Stochastic Optimization Problems, an example
http://edoc.hu-berlin.de/18452/8981
On the Fortet-Mourier metric for the stability of Stochastic Optimization Problems, an example
Strugarek, Cyrille
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We consider the use of the Fortet-Mourier metric between two probability measures to bound the error term made by an approximated solution of a stochastic program. After a short analysis of usual stability arguments, we propose a simple example of stochastic program which enlightens the importance of the information structure. As a conclusion, we underline the need to take into account both the probability measure and the information structure in the discretization of a stochastic program.
2004-12-27T00:00:00ZTwo-stage integer programs with stochastic right-hand sides
http://edoc.hu-berlin.de/18452/8980
Two-stage integer programs with stochastic right-hand sides
Kong, Nan; Schaefer, Andrew J.; Hunsaker, Brady
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms for finding the value functions. To solve the reformulation after obtaining the value functions, we develop a global branch-and-bound approach and a level-set approach to find an optimal tender. We show that our method can solve randomly generated instances that are several orders of magnitude larger than those found in the literature.
2004-10-02T00:00:00ZA class of stochastic programs with decision dependent uncertainty
http://edoc.hu-berlin.de/18452/8979
A class of stochastic programs with decision dependent uncertainty
Goel, Vikas; Grossmann, Ignacio E.
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
The standard approach to formulating stochastic programs is based on the assumption that the stochastic process is independent of the optimization decision. We address a class of problems where the optimization decisions influence the time of information discovery for a subset of the uncertain parameters. We extentd the standard modeling approach by presenting a disjunctive programming formulation that accommodates stochastic programs for this class of ploblems. A set of theoretical properties that lead to reduction in the size of the model is identified. A Lagrange duality based branch and bound algorithm is also presented.
2004-10-02T00:00:00ZVariance reduction in sample approximations of stochastic programs
http://edoc.hu-berlin.de/18452/8978
Variance reduction in sample approximations of stochastic programs
Koivu, Matti
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In high dimensional numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to MC. It seems thus natural to use RQMC methods in sample approximations of stochastic programs. It is shown, that RQMC methods produce epi-convergent approximations of the original problem. RQMC and MC methods are compared numerically in five different portfolio management models. In the tests, RQMC methods outperform MC sampling substantially reducing the sample variance and bias of optimal values in all the considered problems.
2004-10-02T00:00:00Z