Skip to main content

Monte-Carlo Simulations for Stochastic Optimization

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Keywords

Solution Procedures

Establishing Solution Quality

Variance Reduction Techniques

Theoretical Justification for Sampling

See also

References

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aitchison J, Silvey SD (1958) Maximum-likelihood estimation of parameters subject to restraints. Ann Math Statist 29:813–828

    Article  MathSciNet  MATH  Google Scholar 

  2. Artstein Z, Wets RJ-B (1994) Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. SIAM J Optim 4:537–550

    Article  MathSciNet  MATH  Google Scholar 

  3. Asmussen S, Glynn PW, Thorisson H (1992) Stationary detection in the initial transient problem. ACM Trans Modeling and Computer Simulation 2:130–157

    Article  MATH  Google Scholar 

  4. Attouch H, Wets RJ-B (1981) Approximation and convergence in nonlinear optimization. In: Mangasarian O, Meyer R, Robinson S (eds) Nonlinear Programming, vol 4. Acad Press, New York, pp 367–394

    Google Scholar 

  5. Bailey TG, Jensen PA, Morton DP (1999) Response surface analysis of two-stage stochastic linear programming with recourse. Naval Res Logist 46:753–778

    Article  MathSciNet  MATH  Google Scholar 

  6. Beale EML (1955) On minimizing a convex function subject to linear inequalities. J Royal Statist Soc 17B:173–184

    MathSciNet  Google Scholar 

  7. Birge JR (1985) Decomposition and partitioning methods for multistage stochastic linear programs. Oper Res 33:989–1007

    Article  MathSciNet  MATH  Google Scholar 

  8. Birge JR (1997) Stochastic programming computation and applications. INFORMS J Comput 9:111–133

    Article  MathSciNet  MATH  Google Scholar 

  9. Birge JR, Donohue CJ, Holmes DF, Svintsitski OG (1996) A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs. Math Program 75:327–352

    MathSciNet  Google Scholar 

  10. Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, Berlin

    MATH  Google Scholar 

  11. Box GEP, Draper NR (1987) Empirical model-building and response surfaces. Wiley, New York

    MATH  Google Scholar 

  12. Broadie M, Glasserman P (1997) Pricing American-style options using simulation. J Econom Dynam Control 21:1323–1352

    Article  MathSciNet  MATH  Google Scholar 

  13. Cariño DR, Kent T, Meyers DH, Stacy C, Sylvanus M, Turner AL, Watanabe K, Ziemba WT (1994) The Russell-Yasuda Kasia model: An asset/liability model for a Japanese insurance company using multistage stochastic programming. Interfaces 24:29–49

    Article  Google Scholar 

  14. Dantzig GB (1955) Linear programming under uncertainty. Managem Sci 1:197–206

    MathSciNet  MATH  Google Scholar 

  15. Dantzig GB, Glynn PW (1990) Parallel processors for planning under uncertainty. Ann Oper Res 22:1–21

    Article  MathSciNet  MATH  Google Scholar 

  16. Dantzig GB, Glynn PW, Avriel M, Stone JC, Entriken R, Nakayama M (1989) Decomposition techniques for multi-area generation and transmission planning under uncertainty. Report Electric Power Res Inst EPRI 2940-1

    Google Scholar 

  17. Dempster MAH, Thompson RT (1999) EVPI-based importance sampling solution procedures for multistage stochastic linear programmes on parallel MIMD architectures. Ann Oper Res 90:161–184

    Article  MathSciNet  MATH  Google Scholar 

  18. Dupačová J (1991) On non-normal asymptotic behavior of optimal solutions for stochastic programming problems and on related problems of mathematical statistics. Kybernetika 27:38–51

    MathSciNet  MATH  Google Scholar 

  19. Dupačová J, Wets RJ-B (1988) Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. Ann Statist 16:1517–1549

    Article  MathSciNet  MATH  Google Scholar 

  20. Edirisinghe C, Ziemba WT (1996) Implementing bounds-based approximations in convex-concave two-stage stochastic programming. Math Program 75:295–325

    MathSciNet  Google Scholar 

  21. Ensor KB, Glynn PW (1997) Stochastic optimization via grid search. In: Yin GG, Zhang Q (eds) Mathematics of Stochastic Manufacturing Systems, vol 33. Lect Appl Math Amer Math Soc, Providence, pp 89–100

    Google Scholar 

  22. Ensor KB, Glynn PW (2000) Simulating the maximum of a random walk. J Statist Planning Inference 85:127–135

    Article  MathSciNet  MATH  Google Scholar 

  23. Ermoliev Y (1988) Stochastic quasigradient methods. In: Ermoliev Y, Wets RJ-B (eds) Numerical Techniques for Stochastic Optimization. Springer, Berlin, pp 141–185

    Google Scholar 

  24. Frauendorfer K (1992) Stochastic two-stage programming. of Lecture Notes Economics and Math Systems, vol 392. Springer, Berlin

    MATH  Google Scholar 

  25. Fu MC (1994) Optimization via simulation: A review. Ann Oper Res 53:199–248

    Article  MathSciNet  MATH  Google Scholar 

  26. Futschik A, Pflug GCh (1997) Optimal allocation of simulation experiments in discrete stochastic optimization and approximative algorithms. Europ J Oper Res 101:245–260

    Article  MATH  Google Scholar 

  27. Glasserman P (1991) Gradient estimation via perturbation analysis. Kluwer, Dordrecht

    MATH  Google Scholar 

  28. Glynn PW (1989) Optimization of stochastic systems via simulation. In: Proc 1989 Winter Simulation Conf, pp 90–105

    Google Scholar 

  29. Glynn PW (1990) Likelihood ratio gradient estimation for stochastic systems. Comm ACM 33(10):75–84

    Article  Google Scholar 

  30. Higle JL (1998) Variance reduction and objective function evaluation in stochastic linear programs. INFORMS J Comput 10:236–247

    Article  MathSciNet  MATH  Google Scholar 

  31. Higle JL, Sen S (1991) Statistical verification of optimality conditions for stochastic programs with recourse. Ann Oper Res 30:215–240

    Article  MathSciNet  MATH  Google Scholar 

  32. Higle JL, Sen S (1991) Stochastic decomposition: An algorithm for two-stage linear programs with recourse. Math Oper Res 16:650–669

    Article  MathSciNet  MATH  Google Scholar 

  33. Higle JL, Sen S (1996) Duality and statistical tests of optimality for two stage stochastic programs. Math Program 75:257–275

    MathSciNet  Google Scholar 

  34. Higle JL, Sen S (1996) Stochastic decomposition: A statistical method for large scale stochastic linear programming. Kluwer, Dordrecht

    MATH  Google Scholar 

  35. Ho YC, Cao XR (1991) Perturbation analysis of discrete event dynamic systems. Kluwer, Dordrecht

    MATH  Google Scholar 

  36. Huber PJ (1967) The behavior of maximum likelihood estimates under nonstandard conditions. In: Proc Fifth Berkeley Symp Math Stat Probab, pp 221–233

    Google Scholar 

  37. Infanger G (1992) Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs. Ann Oper Res 39:69–95

    Article  MathSciNet  MATH  Google Scholar 

  38. Infanger G (1993) Planning under uncertainty: Solving large-scale stochastic linear programs. Sci Press Ser. Boyd & Fraser, Danvers

    Google Scholar 

  39. Jacobs J, Freeman G, Grygier J, Morton D, Schultz G, Staschus K, Stedinger J (1995) SOCRATES: A system for scheduling hydroelectric generation under uncertainty. Ann Oper Res 59:99–133

    Article  MathSciNet  MATH  Google Scholar 

  40. Jonsbråten TW, Wets RJ-B, Woodruff DL (1998) A class of stochastic programs with decision dependent random elements. Ann Oper Res 82:83–106

    Article  MathSciNet  MATH  Google Scholar 

  41. Kall P (1986) Approximation to optimization problems: An elementary review. Math Oper Res 11:9–18

    Article  MathSciNet  MATH  Google Scholar 

  42. Kall P (1987) On approximations and stability in stochastic programming. In: Guddat J, Jongen HTh, Kummer B, Nožička F (eds) Parametric Optimization and Related Topics. Akad Verlag, Berlin, pp 387–407

    Google Scholar 

  43. Kall P, Ruszczyński A, Frauendorfer K (1988) Approximation techniques in stochastic programming. In: Ermoliev Y, Wets RJ-B (eds) Numerical Techniques for Stochastic Optimization. Springer, Berlin, 33–64

    Google Scholar 

  44. King AJ, Rockafellar RT (1993) Asymptotic theory for solutions in statistical estimation and stochastic programming. Math Oper Res 18:148–162

    Article  MathSciNet  MATH  Google Scholar 

  45. King AJ, Takriti S, Ahmed S (1997) Issues in risk modeling for multi-stage systems. IBM Res Report RC 20993

    Google Scholar 

  46. King AJ, Wets RJ-B (1991) Epi-consistency of convex stochastic programs. Stochastics 34:83–91

    MathSciNet  MATH  Google Scholar 

  47. Kleijnen JPC, Groenendaal WVan (1992) Simulation: A statistical perspective. Wiley, New York

    MATH  Google Scholar 

  48. Krishna AS (1993) Enhanced algorithms for stochastic programming. SOL Report Dept Oper Res Stanford Univ 93–8

    Google Scholar 

  49. Kushner HJ, Yin GG (1997) Stochastic approximation algorithms and applications. Springer, Berlin

    MATH  Google Scholar 

  50. L'Ecuyer P, Giroux N, Glynn PW (1994) Stochastic optimization by simulation: numerical experiments with the M/M/1 queue in steady-state. Managem Sci 40:1245–1261

    MATH  Google Scholar 

  51. Mak WK, Morton DP, Wood RK (1999) Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper Res Lett 24:47–56

    Article  MathSciNet  MATH  Google Scholar 

  52. Pflug GCh, Ruszczyński A, Schultz R (1998) On the Glivenko–Cantelli problem in stochastic programming: Linear recourse and extensions. Math Oper Res 23:204–220

    Article  MathSciNet  MATH  Google Scholar 

  53. Plambeck EL, Fu B-R, Robinson SM, Suri R (1996) Sample-path optimization of convex stochastic performance functions. Math Program 75:137–176

    MathSciNet  Google Scholar 

  54. Prékopa A (1995) Stochastic programming. Kluwer, Dordrecht

    Google Scholar 

  55. Robinson SM (1996) Analysis of sample-path optimization. Math Oper Res 21:513–528

    Article  MathSciNet  MATH  Google Scholar 

  56. Robinson SM, Wets RJ-B (1987) Stability in two-stage stochastic programming. SIAM J Control Optim 25:1409–1416

    Article  MathSciNet  MATH  Google Scholar 

  57. Rubinstein RY, Shapiro A (1993) Discrete event systems: Sensitivity and stochastic optimization by the score function method. Wiley, New York

    MATH  Google Scholar 

  58. Ruszczyński A (1986) A regularized decomposition method for minimizing a sum of polyhedral functions. Math Program 35:309–333

    Article  MATH  Google Scholar 

  59. Schruben LW, Margolin BH (1978) Pseudorandom number assignment in statistically designed simulation and distribution sampling experiments. J Amer Statist Assoc 73:504–525

    Article  MathSciNet  MATH  Google Scholar 

  60. Schultz R (1995) On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Math Program 70:73–89

    MathSciNet  Google Scholar 

  61. Sen S, Doverspike RD, Cosares S (1994) Network planning with random demand. Telecommunication Systems 3:11–30

    Article  Google Scholar 

  62. Shapiro A (1989) Asymptotic properties of statistical estimators in stochastic programming. Ann Statist 17:841–858

    Article  MathSciNet  MATH  Google Scholar 

  63. Shapiro A, Homem-de-Mello T (1998) A simulation-based approach to two-stage stochastic programming with recourse. Math Program 81:301–325

    MathSciNet  Google Scholar 

  64. Slyke RM Van, Wets RJ-B (1969) L-Shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17:638–663

    Article  MathSciNet  MATH  Google Scholar 

  65. Tew JD (1995) Simulation metamodel estimation using a combined correlation-based variance reduction technique for first and higher-order metamodels. Europ J Oper Res 87:349–367

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Morton, D.P., Popova, E. (2008). Monte-Carlo Simulations for Stochastic Optimization . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_404

Download citation

Publish with us

Policies and ethics