| Title:
|
On the stability in stochastic programming: the case of individual probability constraints (English) |
| Author:
|
Kaňková, Vlasta |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
33 |
| Issue:
|
5 |
| Year:
|
1997 |
| Pages:
|
525-546 |
| . |
| Category:
|
math |
| . |
| MSC:
|
90C15 |
| MSC:
|
90C31 |
| idZBL:
|
Zbl 0908.90198 |
| idMR:
|
MR1603961 |
| . |
| Date available:
|
2009-09-24T19:11:15Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125398 |
| . |
| Reference:
|
[1] Z. Artstein: Sensitivity with respect to the underlying information in stochastic programming.J. Comput. Appl. Math. 56 (1994), 127-136. MR 1338640 |
| Reference:
|
[2] B. Bank J. Guddat D. Klatte R. Kummer, R. Tammer: Non-Linear Parametric Optimization.Akademie-Verlag, Berlin 1982. |
| Reference:
|
[3] P. Billingsley: Convergence of Probability Measures.Wiley, New York 1977. MR 0233396 |
| Reference:
|
[4] J. Dupačová: Stability in stochastic programming--probability constraints.In: Proceedings of the International Conference on Stochastic Optimization, Kiev 1984 (V. I. Arkin, A. Shiryaev and R. J.-B. Wets, eds., Lecture Notes in Control and Information Sciences 81), Springer-Verlag, Berlin 1986, pp. 314-324. MR 0890995 |
| Reference:
|
[5] J. Dupačová: Stability and sensitivity analysis for stochastic programming.Annals of Operations Research 27 (1990), 115-142. MR 1088990 |
| Reference:
|
[6] J. Dupačová: On interval estimates for optimal value of stochastic programs.In: System Modelling and Optimization: Proceedings of the 15th IFIP Conference (P. Kall, ed., Lecture Notes in Control and Information Sciences 180), Springer-Verlag, Berlin 1992, pp. 556-563. MR 1182372 |
| Reference:
|
[7] N. Gröwe, W. Römisch: A stochastic programming model for optimal power dispatch: Stability and numerical treatment.In: Stochastic Optimization -- Numerical Methods and Technical Applications (K. Marti, ed., Lecture Notes in Economics and Mathematical Systems 379), Springer-Verlag, Berlin 1992, pp. 111-139. |
| Reference:
|
[8] W. Hoeffding: Probability inequalities for sums of bounded random variables.J. Amer. Statist. Assoc. 38 (1963), 13-30. Zbl 0127.10602, MR 0144363 |
| Reference:
|
[9] P. Kall: On approximation and stability in stochastic programming.In: Parametric Optimization and Related Topics (J. Guddat, H. Th. Jongen, B. Kummer and F. Nožička, eds.), Akademie-Verlag, Berlin 1987, pp. 387-407. MR 0909741 |
| Reference:
|
[10] P. Kall: Stochastic Linear Programming.Springer-Verlag, Berlin--Heildelberg--New York 1976. Zbl 0317.90042, MR 0446504 |
| Reference:
|
[11] Y. M. Kaniovski A. J. King, R. J.-B. Wets: Probabilistic bounds (via large deviations) for the solution of stochastic programming.Annals of Operations Research 26 (1995), 189-208. MR 1339792 |
| Reference:
|
[12] V. Kaňková: An approximative solution of a stochastic optimization problem.In: Trans. Eighth Prague Conference, Academia, Prague 1978, pp. 327-332. MR 0536792 |
| Reference:
|
[13] V. Kaňková: Uncertainty in stochastic programming.In: Proceedings of the International Conference on Stochastic Optimization, Kiev 1984 (V. I. Arkin, A. Shiryaev and R. J.-B. Wets, eds., Lecture Notes in Control and Information Sciences 81), Springer-Verlag, Berlin 1986, pp. 393-401. MR 0891003 |
| Reference:
|
[14] V. Kaňková: On the convergence rate of empirical estimates in chance constrained stochastic programming.Kybernetika 26 (1990), 6, 449-451. MR 1089809 |
| Reference:
|
[15] V. Kaňková: On the stability in stochastic programming -- generalized simple recourse problems.Informatica 5 (1994), 1-2, 55-78. MR 1358237 |
| Reference:
|
[16] V. Kaňková: A note on estimates in stochastic programming.J. Comput. Appl. Math. 56 (1994), 97-112. MR 1338638 |
| Reference:
|
[17] V. Kaňková: On stability in two-stage stochastic nonlinear programming.In: Proceedings of the Fifth Prague Symposium (P. Mandl and M. Hušková, eds.). Springer-Verlag, Berlin 1994, pp. 329-340. MR 1311951 |
| Reference:
|
[18] V. Kaňková: A note on objective functions in multistage stochastic programming problems.In: Proceedings of the 17th IFIP TC7 Conference on System Modelling and Optimization, Prague 1995 (J. Doležal and J. Fidler, eds.). Chapman Hall, London--Glasgow--New York--Tokyo 1995, pp. 582-589. MR 1471302 |
| Reference:
|
[19] V. G. Karmanov: Mathematical Programming.Nauka, Moskva 1975. (In Russian.) Zbl 0349.90075, MR 0411559 |
| Reference:
|
[20] A. Prekopa: Stochastic Programming.Akadémiai Kiadó, Budapest and Kluwer Publisher, Dordrecht 1995. Zbl 0863.90116, MR 1375234 |
| Reference:
|
[21] W. Römisch, A. Wakolbinger: Obtaining convergence rates for approximation in stochastic programming.In: Parametric Optimization and Related Topics (J. Guddat, H. Th. Jongen, B. Kummer and F. Nožička, eds.), Akademie-Verlag, Berlin 1987, pp. 327-343. MR 0909737 |
| Reference:
|
[22] W. Römisch, R. Schulz: Distribution sensitivity in stochastic programming.Mathematical Programming 50 (1991), 197-226. MR 1103933 |
| Reference:
|
[23] W. Römisch, R. Schulz: Stability analysis for stochastic programs.Annals of Operations Research 30 (1991), 569-588. MR 1118900 |
| Reference:
|
[24] W. Römisch, R. Schulz: Lipschitz stability of stochastic programs with complete recourse.SIAM J. Optimization 6 (1996), 531-547. MR 1387338 |
| Reference:
|
[25] G. Salinetti, R. J.-B. Wets: On the convergence of closed-valued measurable multifunctions.Trans. of the American Society 266 (1981), 1, 275-289. Zbl 0501.28005, MR 0613796 |
| Reference:
|
[26] G. Salinetti: Approximations for chance-constrained stochastic programming problems.Stochastics 10 (1983), 157-179. MR 0727452 |
| Reference:
|
[27] R. Schulz: Rates of convergence in stochastic programs with complete integer recourse.SIAM J. Optimization 6 (1996), 4, 1138-1152. MR 1416533 |
| Reference:
|
[28] R. S. Tarasenko: On the estimation of the convergence rate of the adaptive random search method.Problémy slučajnogo poiska (1980), 8, 162-185. (In Russian.) Zbl 0446.90072 |
| Reference:
|
[29] A. B. Tsybakov: Error bounds for the methods of minimization of empirical risk.Problémy Peredachi Informatsii 17 (1981), 50-61. (In Russian.) MR 0647424 |
| Reference:
|
[30] S. Vogel: Stability results for stochastic programming problems.Optimization 19 (1988), 269-288. Zbl 0649.90078, MR 0948397 |
| Reference:
|
[31] K. Yoshihara: Weekly Dependent Sequences and Their Applications. Vol. 1: Summation Theory for Weekly Dependent Sequences.Sanseido, Tokyo 1992. MR 1426601 |
| . |
