Skip to main content

Stochastic Bilevel Programs

SBP

  • Reference work entry
Encyclopedia of Optimization
  • 727 Accesses

Article Outline

Keywords

Principal Features of Bilevel Programs

Examples of Bilevel Programs

Properties of the Stochastic Bilevel Program

Algorithms for Stochastic Bilevel Programs

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. Birge JR, Louveaux F (1997) Stochastic programming. Springer, Berlin

    MATH  Google Scholar 

  2. Christiansen S, Patriksson M, Wynter L (2001) Stochastic bilevel programming in structural optimization. Structural Optim

    Google Scholar 

  3. Facchinei F, Jiang H, Qi L (1999) A smoothing method for mathematical programs with equilibrium constraints. Math Program 85:107–134

    Article  MathSciNet  MATH  Google Scholar 

  4. Facchinei F, Soares J (1997) A new merit function for nonlinear complementarity problems and a related algorithm. SIAM J Optim 7:225–247

    Article  MathSciNet  MATH  Google Scholar 

  5. Geoffrion AM (1970) Elements of large-scale mathematical programming. Managem Sci 16:652–691

    MathSciNet  Google Scholar 

  6. Harker PT, Choi S-C (1991) A penalty function approach for mathematical programs with variational inequality constraints. Inform and Decision Techn 17:41–50

    MathSciNet  MATH  Google Scholar 

  7. Hogan WW (1973) Directional derivatives for extremal-value functions with applications to the completely convex case. Oper Res 21:188–209

    Article  MathSciNet  MATH  Google Scholar 

  8. Larsson T, Patriksson M (1994) A class of gap functions for variational inequalities. Math Program 64:53–79

    Article  MathSciNet  Google Scholar 

  9. Marcotte P, Zhu D (1996) Exact and inexact penalty methods for the generalized bilevel programming problem. Math Program 74:141–157

    MathSciNet  Google Scholar 

  10. Migdalas A, Pardalos PM, Varbrand P (eds) (1998) Multilevel optimization: Algorithms and applications. Kluwer, Dordrecht

    MATH  Google Scholar 

  11. Outrata J, Zowe J (1995) A numerical approach to optimization problems with variational inequality constraints. Math Program 68:105–130

    MathSciNet  Google Scholar 

  12. Patriksson M, Wynter L (1999) Stochastic mathematical programs with equilibrium constraints. Oper Res Lett 25:159–167

    Article  MathSciNet  MATH  Google Scholar 

  13. Robinson SM (1980) Strongly regular generalized equations. Math Oper Res 5:43–62

    Article  MathSciNet  MATH  Google Scholar 

  14. Robinson SM (1991) An implicit-function theorem for a class of nonsmooth functions. Math Oper Res 16:282–309

    Article  Google Scholar 

  15. Shimizu K, Ishizuka Y, Bard J (1996) Nondifferentiable and two-level mathematical programming. Kluwer, Dordrecht

    Google Scholar 

  16. Wets RJ-B (1989) Stochastic programming. In: Nemhauser GL, Rinnooy Kan AHG, Todd MJ (eds) Handbook Oper. Res. and Management Sci., vol 1. North-Holland, Amsterdam, pp 573–629

    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

Wynter, L. (2008). Stochastic Bilevel Programs . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_646

Download citation

Publish with us

Policies and ethics