Estimated stochastic programs with chance constraints

European Journal of Operational Research

Volumn 101, Issue 2, 1997, Pages 285-305

  Gröwe, Nicole ^a  

^a ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Asymptotic stability; Large deviations; Probabilistic constraints; Stochastic programming

Indexed keywords

OPERATIONS RESEARCH; PROBABILITY; RANDOM PROCESSES; REGRESSION ANALYSIS; STABILITY; STATISTICAL METHODS;

LARGE DEVIATIONS; PROBABILISTIC CONSTRAINTS;

MATHEMATICAL PROGRAMMING;

EID: 0031224379     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(96)00398-0     Document Type: Article

References (55)

1. R.E. Barlow, D.J. Bartholomew, J.M. Bremner, H.D. Brunk, Statistical Inference Under Order Restriction, John Wiley and Sons, New York, 1972.
2. R.E. Barlow, W.R. van Zwet, Asymptotic properties of isotonic estimators for the generalized failure rate function. Part I: Strong consistency, in: M.L. Puri (Ed.), Nonparametric Techniques in Statistical Inference, Cambridge University Press, 1970, pp. 159-176.
3. R.E. Barlow, W.R. van Zwet, Asymptotic properties of isotonic estimators for the generalized failure rate function. Part II: Asymptotic distribution, Technical Report, University of California, Berkeley, 1969.
4. R.E. Barlow, W.R. van Zwet, Comparison of several estimators of the failure rate function, Technical Report, University of California, Berkeley, 1969.
5. R.N. Bhattacharya, R. Ranga Rao, Normal Approximation and Asymptotic Expensions, John Wiley and Sons, New York, 1976.
6. R.E. Bixby, E. Boyd, Using the CPLEX callable library, Manual distributed by the Cplex Optimization Inc., 7710-T Cherry Park, Houston TX, 1994.
7. C. Borell, Convex set-functions in d-spaces, Periodica Math. Hungarica 6 (1975) 111-136.
8. H.J. Brascamp, E.H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, Journal of Functional Analysis 22 (1976) 366-389.
9. A. Charnes aud W.W. Cooper, Chance constrained programming, Management Science 6 (1959) 73-89.
10. R.M. Dudley, Real Analysis and Probability, Wadsworth and Brooks/Cole Advanced Books and Software, 1989.
11. J. Dupačová, Stability in stochastic programming - Probabilistic constraints, in: A. Shiraev, R.J.B. Wets (Eds.), Stochastic Optimization, Lecture Notes in Control and Information Sciences, Vol. 81, Springer-Verlag, Berlin, 1986, pp. 314-325.
12. J. Dupačová, Stability and sensitivity analysis for stochastic programming, Annals of Operations Research 27 (1990) 115-142.
13. J. Dupačová, A. Gaivoronski, Z. Kos, T. Szantai, Stochastic programming in water resources planning: A case study and a comparison of solution techniques, Working Paper WP-86-40, International Institute for Applied Systems Analysis Laxenburg, Austria, 1986.
14. J.H. Ellis, Integrating multiple long range transport models into optimization methodologies for acid rain policy analysis, European Journal of Operational Research 46 (1990) 313-321.
15. Y.M. Ermoliev, R.J.-B. Wets (Eds.), Numerical Techniques for Stochastic Optimization, Springer-Verlag, Berlin, 1988.
16. P. Gänssler, W. Stute, Wahrscheinlichkeitstheorie, Springer-Verlag, Berlin, 1977.
17. N. Gröwe, Numerical Solution and Asymptotic Analysis of Stochastic Programs, Ph.D. Dissertation, Institut für Mathematik, Humboldt-Universität zu Berlin, Germany, 1995.
18. J.M. Guldman, Chance-constrained dynamic model of air quality management, Journal of Environmental Engineering 114 (1988) 1116-1135.
19. R. Henrion, W. Römisch, Metric regularity and quantitative stability in stochastic programs with probabilistic constraints, Preprint 96-2, Institut für Mathematik, Humboldt-Universität zu Berlin, Germany, 1996.
20. P. Kall, On approximations and stability in stochastic programming, in: J. Guddat, H.Th. Jongen, B. Kummer, F. Nožička (Eds.), Parametric Optimization and Related Topics, Akademie-Verlag, Berlin, 1987, pp. 77-86.
21. V. Kaňková, On the convergence rate of empirical estimates in chance constrained stochastic programming, Kybernetika 26 (1990) 449-461.
22. V, Kaňková, A note on estimates in stochastic programming, Journal of Computational and Applied Mathematics 56 (1994) 97-112.
23. J. Kiefer, J. Wolfowitz, Asymptotically minimax estimation of concave and convex distribution functions, Z. Wahrscheinlichkeitstheorie verw. Gebiete 34 (1976) 73-85.
24. A.J. King, Stochastic programming problems: Examples from the literature, in: [15], pp. 543-567.
25. D. Klatte, On quantitative stability for non-isolated minima, Control and Cybernetics 23 (1994) 183-200.
26. K. Marti (Ed.), Stochastic Optimization - Numerical Methods and Technical Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 379, Springer-Verlag, Berlin, 1992.
27. K. Marti, Stochastic optimization in structural design, Zeitschrift für Angewandte Mathematik und Mechanik 72 (1992) T452-T464.
28. P. Massart, The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality, Annals of Probability 18 (1990) 1269-1283.
29. J. Mayer, Computational techniques for probabilistic constrained optimization problems, in: [26], pp. 141-159.
30. B.L. Miller, H.M. Wagner, Chance constrained programming with joint constraints, Operations Research 13 (1965) 930-945.
31. V.I. Norkin, The analysis and optimization of probability functions, Working Paper WP-93-6, International Institute for Applied Systems Analysis Laxenburg, Austria, 1993.
32. P. Rao, Estimation for distributions with monotone failure rate, Annals of Statistics 41 (1970) 507-519.
33. A. Prékopa, Logarithmic concave measures with application to stochastic programming, Acta Sci. Math. 32 (1971) 301-316.
34. A. Prékopa, S. Ganczer, I. Deak aud K. Patyi, The STABIL stochastic programming model and its experimental application to the electricity production in Hungary, in: M.A.H. Dempster (Ed.), Stochastic Programming, Academic Press, London, 1980, pp. 369-385.
35. A. Prékopa, Stochastic Programming, Kluwer Academic Publishers, Dordrecht, 1995.
36. A. Prékopa, T. Szántai, Flood control reservoir system design using stochastic programming, Mathematical Programming Study 9 (1983) 138-151.
37. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C - The Art of Scientific Computing, 2nd Edition, Cambridge University Press, 1992.
38. C.S. ReVelle, J. Gundelach Linear decision rules in reservoir management and design - 4. A rule that minimizes output variance, Water Resources Research 6 (1975) 197-203.
39. S.M. Robinson, Regularity and stability for convex multivalued functions, Mathematics of Operations Research 1 (1976) 130-143.
40. R.T. Rockafellar, Integral functionals, normal integrands and measurable selections, in: G.P. Gossez et al. (Eds.), Nonlinear Operators and the Calculus of Variations, Lecture Notes in Mathematics, Vol. 543, Springer-Verlag, New York 1976, pp. 157-207.
41. Y. Rinott, On convexity of measures, Annals of Probability 4 (1976) 1020-1026.
42. T. Robertson, F.T. Wright, R.L. Dykstra, Order Restricted Statistical Inference, John Wiley and Sons, New York, 1988.
43. W. Römisch, R. Schultz, Distribution sensitivity in stochastic programming, Mathematical Programming 50 (1991) 197-226.
44. W. Römisch, R. Schultz, Stability analysis of stochastic programs, Annals of Operations Research 30 (1991) 241-266.
45. W. Römisch, R. Schultz, Distribution sensitivity for certain classes of chance-constrained models with application to power dispatch, Journal of Optimization Theory and Applications 71 (1991) 569-588.
46. G. Salinetti, Approximations for chance-constrained programming problems, Stochastics 10 (1983) 157-179.
47. S. Sen, Relaxation for chance-constrained programs with discrete random variables, Operations Research Letters 11 (1992) 81-86.
48. A. Shapiro, Asymptotic analysis of stochastic programs, Annals of Operations research 30 (1991) 169-186.
49. G.R. Shorack, J. Wellner. Empirical Processes with Applications to Statistics, John Wiley and Sons, New York, 1986.
50. T, Szántai, Calculation of the multivariate probability distribution function values and their gradients, Working Paper WP-87-82, International Institute for Applied Systems Analysis Laxenburg, Austria, 1987.
51. T. Szántai, A computer code for solution of probabilistic-constrained stochastic programming problems, in: [15], pp. 229-235.
52. S. Vogel, Stability results for stochastic programming problems, Optimization 19 (1988) 269-288.
53. J. Wang, Continuity of feasible solution sets of probabilistic constrained programs, Journal of Optimization Theory and Applications 63 (1989) 79-89.
54. G.S. Watson, M.R. Leadbetter, Hazard analysis II, Sankhya A 26 (1964) 101-116.
55. R.J.-B. Wets, Challenges in stochastic programming, Working Paper WP-94-32, International Institute for Applied Systems Analysis Laxenburg, Austria, 1994.