Previous |  Up |  Next

Article

Title: Multistage stochastic programs via autoregressive sequences and individual probability constraints (English)
Author: Kaňková, Vlasta
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 44
Issue: 2
Year: 2008
Pages: 151-170
Summary lang: English
.
Category: math
.
Summary: The paper deals with a special case of multistage stochastic programming problems. In particular, the paper deals with multistage stochastic programs in which a random element follows an autoregressive sequence and constraint sets correspond to the individual probability constraints. The aim is to investigate a stability (considered with respect to a probability measures space) and empirical estimates. To achieve new results the Wasserstein metric determined by ${\cal L}_{1}$ norm and results of multiobjective optimization theory are employed. (English)
Keyword: multistage stochastic programming problem
Keyword: individual probability constraints
Keyword: autoregressive sequence
Keyword: Wasserstein metric
Keyword: empirical estimates
Keyword: multiobjective problems
MSC: 90C15
idZBL: Zbl 1154.90557
idMR: MR2428217
.
Date available: 2009-09-24T20:33:07Z
Last updated: 2012-06-06
Stable URL: http://hdl.handle.net/10338.dmlcz/135841
.
Reference: [1] Birge J. R., Louveuax F.: Introduction to Stochastic Programming.Springer, Berlin 1997 MR 1460264
Reference: [2] Dupačová J.: Multistage stochastic programs: the state-of-the-art and selected bibliography.Kybernetika 31 (1995), 2, 151–174 Zbl 0860.90093, MR 1334507
Reference: [3] Dupačová J., Hurt, J., Štěpán J.: Stochastic Modelling in Economics and Finance.Kluwer, Dordrecht 2002
Reference: [4] Dupačová J., Popela P.: Melt control: Charge optimization via stochastic programming.In: Applications of Stochastic Programming (S. W. Wallace and W. T. Ziemba, eds.), Philadelphia, SIAM and MPS 2005, pp. 277–298 Zbl 1190.90063, MR 2162956
Reference: [5] Chovanec P.: Multistage Stochastic Programming Problems – Application to Unemployment Problem and Restructuralization (in Czech).Diploma Work. Faculty of Mathematics and Physics, Charles University, Prague 2004
Reference: [6] Ehrgott M.: Multicriteria Optimization.Second edition. Springer, Berlin 2005 Zbl 1132.90001, MR 2143243
Reference: [7] Frauendorfer K., Schürle M.: Term structure in multistage stochastic programming: estimation and approximation.Ann. Oper. Res. 100 (2000), 1–4, 185–209
Reference: [8] Geoffrion A. M.: Proper efficiency and the theory of vector maximization.J. Math. Anal. Appl. 22 (1968), 618–630 Zbl 0181.22806, MR 0229453
Reference: [9] Kaňková V.: A Note on multifunction in stochastic programming.In: Stochastic Programming Methods and Technical Applications (K. Marti and P. Kall, eds.), Springer, Berlin 1996 MR 1650784
Reference: [10] Kaňková V.: On the stability in stochastic programming: The case of individual probability constraints.Kybernetika 33 (1997), 5, 525–546 Zbl 0908.90198, MR 1603961
Reference: [11] Kaňková V.: A note on multistage stochastic programming.In: Proc. 11th Joint Czech–Germany–Slovak Conference: Mathematical Methods in Economy and Industry. University of Technology, Liberec 1998, pp. 45–52
Reference: [12] Kaňková V.: A remark on the analysis of multistage stochastic programs, Markov dependence.Z. Angew. Math. Mech. 82 (2002), 781–793 Zbl 1028.90031, MR 1944422
Reference: [13] Kaňková V., Šmíd M.: On approximation in multistage stochastic programs: Markov dependence.Kybernetika 40 (2004), 5, 625–638 MR 2121001
Reference: [14] Kaňková V., Šmíd M.: A Remark on Approximation in Multistage Stochastic Programs; Markov Dependence.Research Report No. 2101, Institute of Information Theory and Automation, Prague 2002
Reference: [15] Kaňková V.: Multistage stochastic decision and economic proceses.Acta Oeconomica Pragensia 13 (2005), 1, 119–127
Reference: [16] Kaňková V., Houda M.: Empirical estimates in stochastic programming.In: Prague Stochastics 2006 (M. Hušková and M. Janžura, eds.), Matfyzpress, Prague 2006, pp. 426–436 Zbl 1162.90528
Reference: [17] Kaňková V., Chovanec P.: Unemployment problem via multistage stochastic programming.In: Proc. Quantitative methods in Economics (Multiple Criteria Decision making XIII) (J. Pekár and M. Lukáčik, eds.), The Slovak Society for Operations Research and University of Economics in Bratislava, Bratislava 2006, pp. 69–76
Reference: [20] Kaňková V.: Empirical Estimates via Stability in Stochastic programming.Research Report No. 2192, Institute of Information Theory and Automation, Prague 2007
Reference: [21] Kaňková V.: Multistage stochastic programs via stochastic parametric optimization.In: Operations Research Proceedings 2007 (J. Kalcsics and S. Nickel, eds.), Springer, Berlin – Heidelberg 2008, pp. 63–68 Zbl 1209.90282
Reference: [22] King A. J.: Stochastic programming problems: examples from the literature.In: Numerical Techniques for Stochastic Optimization Problems (Yu. Ermoliev and J.-B. Wets, eds.), Springer, Berlin 1968, pp. 255–266 MR 0957334
Reference: [23] Kuhn D.: Generalized Bounds for Convex Multistage Stochastic Programs.(Lecture Notes in Economics and Mathematical Systems 548.) Springer, Berlin 2005 Zbl 1103.90069, MR 2103400
Reference: [24] Nowak M. P., Römisch W.: Stochastic Lagrangian relaxation applied to power scheduling in hydro-termal system under uncertainty.Ann. Oper. Res. 100 (2000), 251–272 MR 1843544
Reference: [25] Powell W. B., Topaloglu H.: Stochastic programming in transportation and logistics.In: Stochastic Programming, Handbooks in Operations Research and Management Science, Volume 10 (A. Ruszczyński and A. Shapiro, eds.), Elsevier, Amsterdam 2003, pp. 555–636 MR 2052761
Reference: [26] Prékopa A.: Stochastic Programming.Akadémiai Kiadó, Budapest and Kluwer, Dordrecht 1995 Zbl 1219.90114, MR 1375234
Reference: [27] Römisch W., Schulz R.: Stability of solutions for stochastic programs with complete recourse.Math. Oper. Res. 18 (1993), 590–609 MR 1250562
Reference: [28] Salinetti G.: Approximations for chance constrained programming problems.Stochastics 10 (1983), 157–179 Zbl 0536.90067, MR 0727452
Reference: [29] Serfling J. R.: Approximation Theorems of Mathematical Statistics.Wiley, New York 1980 Zbl 1001.62005, MR 0595165
Reference: [30] Vallander S. S.: Calculation of the Wasserstein distance between probability distributions on the line (in Russian).Theory Probab. Appl. 18 (1973), 784–786 MR 0328982
Reference: [31] Wallace S. W., Fleten S. E.: Stochastic programming models in energy.In: Stochastic Programming, Handbooks in Operations Research and Management Science, Volume 10 (A. Ruszczyński and A. Shapiro, eds.), Elsevier, Amsterdam 2003, pp. 637–677 MR 2052762
Reference: [32] Wallace S. W., Ziemba W. T: Applications of Stochastic Programming.SIAM and MPS, Philadelphia 2005 Zbl 1068.90002, MR 2162941
.

Files

Files Size Format View
Kybernetika_44-2008-2_3.pdf 779.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo