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Bilevel Linear Programming

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Encyclopedia of Optimization

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References

  1. Bard JF (1984) Optimality conditions for the bilevel programming problem. Naval Res Logist Quart 31:13–26

    Article  MathSciNet  MATH  Google Scholar 

  2. Bard JF, Falk JE (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9(1):77–100

    Article  MathSciNet  Google Scholar 

  3. Bard JF, Moore JT (1990) A branch and bound algorithm for the bilevel programming problem. SIAM J Sci Statist Comput 11(2):281–292

    Article  MathSciNet  MATH  Google Scholar 

  4. Bialas WF, Karwan MH (1984) Two-level linear programming. Managem Sci 30(8):1004–1020

    MathSciNet  MATH  Google Scholar 

  5. Candler W, Townsely R (1982) A linear two-level programming problem. Comput Oper Res 9(1):59–76

    Article  MathSciNet  Google Scholar 

  6. Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bilevel programming. SIAM J Sci Statist Comput 13(1):1194–1217

    MathSciNet  MATH  Google Scholar 

  7. Jeroslow RG (1985) The polynomial hierarchy and a simple model for competitive analysis. Math Program 32:146–164

    Article  MathSciNet  MATH  Google Scholar 

  8. Shimizu K, Ishizuka Y, Bard JF (1997) Nondifferentiable and two-level mathematical programming. Kluwer, Dordrecht

    MATH  Google Scholar 

  9. Simaan M (1977) Stackelberg optimization of two-level systems. IEEE Trans Syst, Man Cybern SMC-7(4):554–556

    MathSciNet  Google Scholar 

  10. White DJ, Anandalingam G (1993) A penalty function for solving bi-level linear programs. J Global Optim 3:397–419

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University Texas, Austin, USA

    Jonathan F. Bard

Authors
  1. Jonathan F. Bard
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Bard, J.F. (2008). Bilevel Linear Programming . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_36

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