Stability and scenario trees for multistage stochastic programs

International Series in Operations Research and Management Science

Volumn 150, Issue , 2011, Pages 139-164

  Heitsch, Holger ^a   Römisch, Werner ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84975758765     PISSN: 08848289     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4419-1642-6_7     Document Type: Chapter

References (45)

1. Attouch, H., Wets, R.J.-B.: Quantitative stability of variational systems: III. ε-approximate solutions. Math. Program. 61(1-3), 197-214 (1993)
2. Casey, M., Sen, S.: The scenario generation algorithm for multistage stochastic linear programming. Math. Oper. Res. 30(3), 615-631 (2005)
3. Chiralaksanakul, A., Morton, D.P.: Assessing policy quality in multi-stage stochastic programming. 12-2004, Stochastic Programming E-Print Series, ¡www.speps.org¿ (2005)
4. Corvera Poiré, X.: The scenario generation algorithm formultistage stochastic linear programming. PhD thesis, Department of Mathematics, University of Essex (2005)
5. Dantzig, G.B,: Linear programming under uncertainty. Manage. Sci. 1(3-4), 197-206 (1955)
6. Dantzig, G.B,: Linear Programming and Extensions. Princeton University Press, Princeton, NJ (1963)
7. Dempster, M. A.H.: Sequential importance sampling algorithms for dynamic stochastic programming. Pomi 312, Zap. Nauchn. Semin (2004)
8. Dupačová, J., Consigli, G., Wallace, S.W.: Scenarios for multistage stochastic programs. Ann. Oper. Res. 100(1-4), 25-53 (2000)
9. Dupačová, J., Gröwe-Kuska, N., Römisch, W.: Scenario reduction in stochastic programming: An approach using probability metrics. Math. Program, 95(3), 493-511 (2003)
10. Edirisinghe, N. C.P,: Bound-based approximations in multistage stochastic programming: Nonanticipativity aggregation. Ann. Oper. Res. 85(0), 103-127 (1999)
11. Eichhorn, A., Römisch,W.: Polyhedral risk measures in stochastic programming. SIAM J. Optim. 16(1), 69-95 (2005)
12. Eichhorn, A., Römisch, W., Wegner, I.: Mean-risk optimization of electricity portfolios using multiperiod polyhedral risk measures. IEEE St. Petersburg Power Tech. 1-7 (2005)
13. Eichhorn, W., Römisch, A.: Stability of multistage stochastic programs incorporating polyhedral risk measures. Optimization 57(2), 295-318 (2008)
14. Fabian, M., Habala, P., Hájek, P., Montesinos Santalucia, V., Pelant, J., Zizler, V.: Functional Analysis and Infinite-Dimensional Geometry. CMS Books in Mathematics. Springer, New York, NY (2001)
15. Frauendorfer, K.: Barycentric scenario trees in convex multistage stochastic programming. Math. Program. 75(2), 277-293 (1996)
16. Gröwe-Kuska, N., Heitsch, H., Römisch,W.: Scenario reduction and scenario tree construction for power management problems. In: Borghetti, A., Nucci, C.A., Paolone,M., (eds.) IEEE Bologna Power Tech Proceedings. IEEE (2003)
17. Heitsch, H., Römisch, W.: Scenario reduction algorithms in stochastic programming. Comput. Optim. Appl. 24(2-3), 187-206 (2003)
18. Heitsch, H., Römisch, W.: Scenario tree modelling for multistage stochastic programs. Math. Program. 118(2), 371-406 (2009)
19. Heitsch, H., Römisch, W., Strugarek, C.: Stability of multistage stochastic programs. SIAM J. Optim. 17(2), 511-525 (2006)
20. Higle, J.L., Rayco, B., Sen, S.: Stochastic scenario decomposition for multistage stochastic programs. IMA J. Manage. Math. 21, 39-66 (2010)
21. Hochreiter, R.: Computational Optimal Management Decisions - The case of Stochastic Programming for Financial Management. PhD thesis, University of Vienna, Vienna, Austria (2005)
22. Hochreiter, R., Pflug, G.: Financial scenario generation for stochastic multi-stage decision processes as facility location problem. Ann. Oper. Res. 152(1), 257-272 (2007)
23. Høyland, K., Wallace, S.W.: Generating scenario trees for multi-stage decision problems. Manag. Sci. 47(2), 295-307 (2001)
24. Høyland, K., Kaut, M., Wallace, S.W.: A heuristic for moment-matching scenario generation. Comput. Optim. Appl. 24(2-3), 169-185 (2003)
25. Infanger, G.: Planning under Uncertainty - Solving Large-Scale Stochastic Linear Programs. Boyd & Fraser Danvers, Massachusetts (1994)
26. Kall, P., Mayer, J.: Stochastic Linear Programming. Springer, New York, NY (2005)
27. Kaut, M., Wallace, S.W.: Evaluation of scenario-generation methods for stochastic programming. Pacific J. Optim. 3(2), 257-271 (2007)
28. Kuhn, D.: Generalized Bounds for Convex Multistage Stochastic Programs. Lecture Notes in Economics and Mathematical Systems, vol. 548. Springer, Berlin (2005)
29. Luschgy, H.: Foundations of Quantization for Probability Distributions. Lecture Notes in Mathematics, vol. 1730. Springer, Berlin (2000)
30. Möller, A., Römisch,W.,Weber, K.: Airline network revenue management by multistage stochastic programming. Comput. Manage. Sci. 5(4), 355-377 (2008)
31. Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. CMBS-NSF Regional Conference Series in Applied Mathematics, vol. 63. SIAM, Philadelphia (1992)
32. Pennanen, T.: Epi-convergent discretizations of multistage stochastic programs. Math. Oper. Res. 30(1), 245-256 (2005)
33. Pennanen, T.: Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Math. Program. 116(1-2), 461-479 (2009)
34. Pflug, G.Ch.: Scenario tree generation for multiperiod financial optimization by optimal discretization. Math. Program. 89(2), 251-271 (2001)
35. Rachev, S.T., Römisch,W.: Quantitative stability in stochastic programming: The method of probability metrics. Math. Oper. Res. 27(3), 792-818 (2002)
36. Rockafellar, R.T.: Integral functionals, normal integrands and measurable selections. In: Gossez, J.P., et al., editor, Nonlinear Operators and the Calculus of Variations. Lecture Notes in Mathematics, vol. 543, pp. 157-207. Springer, Berlin (1976)
37. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)
38. Römisch, W., Wets, R.J.-B.: Stability of ε-approximate solutions to convex stochastic programs. SIAM J. Optim. 18(3), 961-979 (2007)
39. Ruszczyński, A., Shapiro, A., (eds.).: Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10. Elsevier, Amsterdam (2003)
40. Schmöller, H.: Modellierung von Unsicherheiten bei der mittelfristigen Stromerzeugungs- und Handelsplanung. Aachener Beiträge zur Energieversorgung, Aachen (2005) Band 103
41. Shapiro, A.: Inference of statistical bounds formultistage stochastic programming problems. Math. Methods. Oper. Res. 58(1), 57-68 (2003)
42. Shapiro, A.: On complexity of multistage stochastic programs. Oper. Res. Lett. 34(1), 1-8 (2006)
43. Shapiro, A.: Stochastic programming approach to optimization under uncertainty. Math. Program. 112(1), 183-220 (2008)
44. Wallace, S.W., Ziemba, W.T., (eds.): Applications of Stochastic Programming. Series in Optimization. MPS-SIAM Philadelphia (2005)
45. Zaanen, A.C.: Linear Analysis. North-Holland, Amsterdam (1953)