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Barycentric Bounds in Stochastic Programming : Theory and Application

The design and analysis of efficient approximation schemes is of fundamental importance in stochastic programming research. Bounding approximations are particularly popular for providing strict error bounds that can be made small by using partitioning techniques. In this article we develop a powerful bounding method for linear multistage stochastic programs with a generalized nonconvex dependence on the random parameters. Thereby, we establish bounds on the recourse functions as well as compact bounding sets for the optimal decisions. We further demonstrate that our bounding methods facilitate the reliable solution of important real-life decision problems. To this end, we solve a stochastic optimization model for the management of non-maturing accounts and compare the bounds on maximum profit obtained with different partitioning strategies.
   
type book chapter (English)
   
keywords stochastic programming, barycentric approximation scheme, bounds
   
book title Stochastic programming: the state of the art in honor of George B. Dantzig
date of appearance 2011
publisher Springer Science+Business Media, LLC (New York, NY)
series title International Series in Operations Research and Management Science (150)
ISBN 978-1-4419-1641-9
page(s) 67-96
citation Frauendorfer, K., Kuhn, D., & Schürle, M. (2011). Barycentric Bounds in Stochastic Programming: Theory and Application. In Stochastic programming: the state of the art in honor of George B. Dantzig (pp. 67-96). New York, NY: Springer Science+Business Media, LLC. - ISBN 978-1-4419-1641-9.