Numerical Techniques in Applied Multistage Stochastic Programming
- 351 Downloads
This contribution deals with the apparent difficulties when solving an optimization problem with random influences by the use of multistage stochastic linear programming. It names specific numerical solution techniques which are suitable for coping with the curse of dimensionality, with increasing scenario trees and associated large-scale LPs. The focus lies on classic decomposition methods which are natural candidates to apply parallelization techniques. In addition, an alternative approach is sketched where the replacement of optimization runs by optimality checks leads to an efficient handling of consecutive discretization steps given some structural requirements arc fulfilled.
KeywordsMultistage stochastic linear programming discretization large-scale linear program numerical techniques
Unable to display preview. Download preview PDF.
- Wets, R. J.-B.: Stochastic programming: Solution techniques and approximation schemes, In: A. Bachem, M. Grötschel and B. Korte (eds), Mathematical Programming: The State-of-the-art 1982, Springer-Verlag, Berlin, 1983, pp. 566–603.Google Scholar
- Birge, J. R.: Using sequential approximations in the L-shaped and generalized programming algorithms for stochastic linear programs, Technical Report 83-12, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, 1983.Google Scholar
- Dantzig, G. B. and Infanger, G.: Large-scale stochastic linear programs — Importance sampling and Benders decomposition, In: Computational and Applied Mathematics, I. Algorithms and Theory, Sel. Rev. Pap. IMACS 13th World Congr., Dublin/Irel. 1991, 1992, pp. 111–120.Google Scholar
- Wittrock, R. J.: Advances in a nested decomposition algorithm for solving staircase linear programs, Technical Report SOL 83-2, Systems Optimization Laboratory, Stanford University, Stanford, CA, 1983.Google Scholar
- Morton, D. P.: An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling, Technical Report NPSOR-94-001, Department of Operations Research, Naval Postgraduate School, Monterey, CA, 1994.Google Scholar
- Rosa, C. and Ruszczyński, A.: On augmented Lagrangian decomposition methods for multistage stochastic programs, Working Paper WP-94-125, IIASA International Institute for Applied Systems Analysis, Laxenburg, Austria, 1994.Google Scholar
- Gondzio, J. and Kouwenberg, R.: High performance computing for asset liability management, Preprint MS-99-004, Department of Mathematics & Statistics, The University of Edinburgh, UK, 1999.Google Scholar
- Gondzio, J.: HOPDM (version 2.12) — A fast LP solver based on a primal-dual interior point method, Europ. J. Oper. Res. 85 (1955), 221–225.Google Scholar
- Marohn, C.: Stochastische mehrstufige lineare Programmierung im Asset & Liability Management, Bank-und finanzwirtschaftliche Forschungen, Bd. 282, Paul Haupt Verlag, Bern, 1998.Google Scholar
- Haarbrücker, G.: Sequentielle Optimierung verfeinerter Approximationen in der mehrstufigen stochastischen linearen Programmierung, Doctoral thesis No. 2410, University of St. Gallen, 2000.Google Scholar
- Frauendorfer, K. and Haarbrücker, G.: Solving sequences of refined multistage stochastic linear programs, Submitted for appearance in Ann. Oper. Res. Google Scholar