Skip to main content
SpringerLink
Log in
Book cover

Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search pp 169–188Cite as

Sample-Path Solutions for Simulation Optimization Problems and Stochastic Variational Inequalities

  • Chapter

Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 9))

Abstract

In this paper, we give an overview of some recent developments in using simulation together with gradient estimation techniques to provide solutions for difficult stochastic optimization problems and stochastic variational inequalities. The basic idea is to observe a fixed sample path (by using the method of common random numbers from the simulation literature), solve the resulting deterministic problem using fast and effective methods from nonlinear programming, and then use the resulting solutions to infer information about the solution of the original stochastic problem. We describe these so-called sample-path methods precisely, review some conditions under which they are known to work, and comment on their potential advantages and limitations. We also illustrate some application areas in which these ideas have been successful.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Correa, R. and Lemaréchal, C. 1993. Convergence of some algorithms for convex minimization Mathematical Programming 62: 261–275.

    Article  Google Scholar 

  2. De Wolf, D. and Smeers, Y. 1997. A stochastic version of a Stackelberg-NashCournot equilibrium model. Management Science 43 (2): 190–197.

    Article  Google Scholar 

  3. Dirkse, S. and Ferris, M. C. 1995a. The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software 5: 123–156.

    Article  Google Scholar 

  4. Dirkse, S. and Ferris, M. C. 1995b. MCPLIB: A collection of nonlinear mixed complementarily problems. Optimization Methods and Software 5: 319–345.

    Article  Google Scholar 

  5. Dontchev, A. and Rockafellar, R. T. 1996. Characterizations of strong regularity for variational inequalities over polyhedral convex sets. SIAM Journal on Optimization 6: 1087–1105.

    Article  Google Scholar 

  6. Ferris, M. C. and Pang, J.-S. 1997. Engineering and economic applications of complementarity problems. Forthcoming in SIAM Review.

    Google Scholar 

  7. Fletcher, R. 1987. Practical Methods of Optimization, 2nd Ed. ( Wiley, Chichester).

    Google Scholar 

  8. Fu, B.-R. 1996. Modeling and analysis of discrete tandem production lines using continuous flow models. Ph. D. Dissertation. Department of Industrial Engineering, University of Wisconsin-Madison, Madison, Wisconsin, USA.

    Google Scholar 

  9. Fu, M. C., and Hu, J.-Q. 1995. Sensitivity Analysis for Monte Carlo Simulation of Option Pricing. Probability in the Engineering and Informational Sciences 9: 417–449.

    Article  Google Scholar 

  10. Gill, P. E., Murray, W., and Wright, M. H. 1981. Practical Optimization ( Academic Press, London).

    Google Scholar 

  11. Glasserman, P. 1991. Gradient Estimation via Perturbation Analysis (Kluwer, Norwell, MA).

    Google Scholar 

  12. Gürkan, G. 1996. Performance optimization in simulation: Sample-path optimization of buffer allocations in tandem lines. Ph.D. Dissertation, Department of Industrial Engineering, University of Wisconsin-Madison, Madison, Wisconsin, USA.

    Google Scholar 

  13. Gürkan, G., Özge, A. Y. and Robinson, S. M. 1996. Sample-path solution of stochastic variational inequalities, with applications to option pricing. In: Proceedings of the 1996 Winter Simulation Conference, eds. J. M. Charnes, D. M. Motrice, D. T. Brunner, and J. J. Swain ( IEEE, Piscataway, New Jersey ), 337–344.

    Google Scholar 

  14. Gürkan, G., Özge, A. Y. and Robinson, S. M. 1997. Sample-path solution of stochastic variational inequalities. Preprint.

    Google Scholar 

  15. Harker, P. T. and Pang, J.-S. 1990. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms, and applications. Mathematical Programming 48: 161–220.

    Article  Google Scholar 

  16. Haurie, A., Zaccour, C., Legrand, J., and Smeers, Y. 1987. A stochastic dynamic Nash-Cournot model for the European gas market. Technical report G-87–24, GERAD, École des Hautes Etudes Commerciales, Montréal, Québec, Canada.

    Google Scholar 

  17. Healy, K. and Schruben, L. W. 1991. Retrospective simulation response optimization. In: Proceedings of the 1991 Winter Simulation Conference, eds. B.L. Nelson, W.D. Kelton and G.M. Clark ( IEEE, Piscataway, New Jersey ), 901–906.

    Chapter  Google Scholar 

  18. Hiriart-Urruty, J.-B. and Lemaréchal, C. 1993a. Convex Analysis and Minimization Algorithms I (Grundlehren der mathematischen Wissenschaften 305, Springer-Verlag, Berlin).

    Google Scholar 

  19. Hiriart-Urruty, J.-B. and Lemaréchal, C. 1993b. Convex Analysis and Minimization Algorithms II (Grundlehren der mathematischen Wissenschaften 306, Springer-Verlag, Berlin).

    Google Scholar 

  20. Ho, Y.-C. and Cao, X.-R. 1991. Perturbation Analysis of Discrete Event Dynamical Systems (Kluwer, Norwell, MA).

    Google Scholar 

  21. Hogan, W. W. 1975. Energy policy models for Project Independence. Computers & Operations Research 2: 251–271.

    Article  Google Scholar 

  22. Hull, J. C. 1993. Options, Futures, and Other Derivative Securities, 2d Ed. (Prentice-Hall, Englewood Cliffs, NJ ).

    Google Scholar 

  23. Josephy, N. H. 1979. Newton’s Method for Generalized Equations and the PIES Energy Model. Ph.D. Dissertation, Department of Industrial Engineering, University of Wisconsin-Madison, Madison, Wisconsin, USA.

    Google Scholar 

  24. Kall, P. 1986. Approximation to optimization problems: An elementary review. Mathematics of Operations Research 11: 9–18.

    Article  Google Scholar 

  25. Kiwiel, K. C. 1990. Proximity control in bundle methods for convex nondifferentiable minimization Mathematical Programming 46: 105–122.

    Article  Google Scholar 

  26. L’Ecuyer, P., Giroux, N. and Glynn, P. W. 1994. Stochastic optimization by simulation: numerical experiments with the M/M/1 queue in the steady-state. Management Science 40: 1245–1261.

    Article  Google Scholar 

  27. Mort, J. and Wright, S. J. 1993. Optimization Software Guide. Frontiers in Applied Mathematics Vol. 14 ( Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania ).

    Google Scholar 

  28. Mulvey, J. M. and Vladimirou, H. 1991. Applying the progressive hedging algorithm to stochastic generalized networks. Annals of Operations Research 31: 399–424.

    Article  Google Scholar 

  29. Özge, A. Y. 1997. Sample-path solution of stochastic variational inequalities and simulation optimization problems. Ph.D. Dissertation, Department of Industrial Engineering, University of Wisconsin-Madison, Madison, Wisconsin, USA.

    Google Scholar 

  30. Plambeck, E. L., Fu, B.-R., Robinson, S. M., and Suri, R. 1993. Throughput optimization in tandem production lines via nonsmooth programming In: Proceedings of the 1993 Summer Computer Simulation Conference, ed. J. Schoen ( Society for Computer Simulation, San Diego, CA ), 70–75.

    Google Scholar 

  31. Plambeck, E. L., Fu, B.-R., Robinson, S. M., and Suri, R. 1996. Sample-path optimization of convex stochastic performance functions. Mathematical Programming. 75: 137–176.

    Google Scholar 

  32. Qi, L., and Sun, J. 1993. A nonsmooth version of Newton’s method. Mathematical Programming 58: 353–367.

    Google Scholar 

  33. Robinson, S. M. 1980. Strongly regular generalized equations. Mathematics of Operations Research 5: 43–62.

    Article  Google Scholar 

  34. Robinson, S. M. 1987. Local epi-continuity and local optimization. Mathematical Programming 37: 208–222.

    Article  Google Scholar 

  35. Robinson, S. M. 1996. Analysis of sample-path optimization Mathematics of Operations Research 21: 513–528.

    Article  Google Scholar 

  36. Rubinstein, R. Y. and Shapiro, A. 1993. Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method ( Wiley, Chichester).

    Google Scholar 

  37. Schramm, H., and Zowe, J. 1990. A version of the bundle idea for minimizing a nonsmooth function: conceptual idea, convergence analysis, numerical results. Technical Report, 209. Mathematisches Institut, Universität Bayreuth, Bayreuth, Germany.

    Google Scholar 

  38. Sellami, H. and Robinson, S. M. 1996. Homotopies based on nonsmooth equations for solving nonlinear variational inequalities. In Nonlinear Optimization and Applications, eds. G. Di Pillo and F. Giannessi ( Plenum Publishing Corp., New York and London ) 329–342.

    Google Scholar 

  39. Sellami, H. and Robinson, S. M. 1997. Implementation of a continuation method for normal maps. Mathematical Programming 76: 563–578.

    Google Scholar 

  40. Stoll, H. R. and Whaley, R. E. 1993. Futures and Options ( South-Western, Cincinnati, OH )

    Google Scholar 

  41. Suri, R. 1989. Perturbation analysis: the state of the art and research issues explained via the GI/G/1 queue. Proceedings of the IEEE 77 (1): 114–137.

    Article  Google Scholar 

  42. Suri, R. and Fu, B.-R. 1994. On using continuous flow lines to model discrete production lines. Discrete Event Dynamic Systems 4: 129–169.

    Article  Google Scholar 

  43. Zowe J. 1989. The BT-algorithm for minimizing a nonsmooth functional subject to linear constraints. In: Nonsmooth Optimization and Related Topics, eds. F. H. Clarke, V. Demyanov, and F. Giannessi (Plenum Publishing Corp, New York ).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CentER for Economic Research, Tilburg University, PO. Box 90153, 5000 LE, Tilburg, The Netherlands

    Gül Gürkan

  2. Information Technology Laboratory, General Electric Company, One Research Circle, Niskayuna, NY, 12309, USA

    A. Yonca Özge

  3. Department of Industrial Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI, 53706-1539, USA

    Stephen M. Robinson

Authors
  1. Gül Gürkan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Yonca Özge
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephen M. Robinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California, Davis, USA

    David L. Woodruff

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media New York

About this chapter

Cite this chapter

Gürkan, G., Özge, A.Y., Robinson, S.M. (1998). Sample-Path Solutions for Simulation Optimization Problems and Stochastic Variational Inequalities. In: Woodruff, D.L. (eds) Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search. Operations Research/Computer Science Interfaces Series, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2807-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-2807-1_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5023-9

  • Online ISBN: 978-1-4757-2807-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation