Skip to main content

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 458))

Abstract

Various aspect of the robust optimization approach [11] are discussed in the context of scenario based stochastic linear programs. The main items are the choice of the model parameter, which can be related to properties of nonlinearly perturbed linear programs [10] or of parametric quadratic programs [1], and an extension of the first results on the robustness of the optimal value with respect to probabilities of the selected scenarios and with respect to out-of-sample scenarios, cf. [5].

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Bank et al.: Non-Linear Parametric Optimization. Akademie-Verlag, Berlin 1982.

    Google Scholar 

  2. R. S. Dembo: Scenario optimization. Annals of Oper. Res. 30 (1991) 63–80.

    Article  Google Scholar 

  3. P. DobiJs: Robust optimization. Diploma thesis, Dept. of Statistics, Charles University, Prague, 1997.

    Google Scholar 

  4. J. Dupačová: Stability and sensitivity analysis for stochastic programming. Annals of Oper. Res. 27 (1990) 115–142.

    Article  Google Scholar 

  5. J. Dupačová: Scenario based stochastic programs: Resistance with respect to sample. Annals of Oper. Res. 64 (1996) 21–38.

    Article  Google Scholar 

  6. J. Dupačová, M. Bertocchi and V. Moriggia: Postoptimality for scenario based financial planning models with an application to bond portfolio management. To appear in: World Wide Asset and Liability Modeling (W. T. Ziemba and J. Mulvey, eds.), Cambridge University Press 1997.

    Google Scholar 

  7. W. H. Evers: A new model for stochastic linear programming. Management Science 13 (1967) 680–693.

    Article  Google Scholar 

  8. E. G. Gol’shtein: Theory of Convex Programming, Translations of Mathematical Monographs 36 (American Mathematical Society, Providence RI, 1972).

    Google Scholar 

  9. A. J. King: Asymmetric risk measures and tracking models for portfolio optimization under uncertainty, Annals of Oper. Res. 45 (1993) 165–178.

    Article  Google Scholar 

  10. O. L. Mangasarian and R. R. Meyer: Nonlinear perturbation of linear programs, SIAM J. on Control and Optimization 17 (1979) 745–752.

    Article  Google Scholar 

  11. J. M. Mulvey, R. J. Vanderbei and S. A. Zenios: Robust optimization of large scale systems, Oper. Res. 43 (1995) 264–281.

    Article  Google Scholar 

  12. H. Vladimirou and S. A. Zenios: Stochastic linear programs with restricted recourse. To appear in EJOR.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dupačová, J. (1998). Reflections on Robust Optimization. In: Marti, K., Kall, P. (eds) Stochastic Programming Methods and Technical Applications. Lecture Notes in Economics and Mathematical Systems, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45767-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45767-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63924-4

  • Online ISBN: 978-3-642-45767-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics