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Integer Programming Duality

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Encyclopedia of Optimization

Article Outline

Keywords

Linear Programming Duality

Integer Programming

Surrogate Duality

Lagrangian Duality

Superadditive Duality

Solving the Superadditive Dual

Another Functional Dual

Inference Duality

Conclusions

See also

References

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References

  1. Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming: Theory and algorithms, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  2. Blair CE, Jeroslow R (1977) The value function of a mixed integer program 1. Discret Math 19:121–138

    Article  MathSciNet  MATH  Google Scholar 

  3. Blair CE, Jeroslow R (1982) The value function of a mixed integer program. Math Program 23:237–273

    Article  MathSciNet  MATH  Google Scholar 

  4. Dawande M, Hooker JN Inference-based sensitivity analysis for mixed intetger linear programming. Oper Res (to appear).

    Google Scholar 

  5. Everett III H (1963) Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Oper Res 11:399–417

    MATH  Google Scholar 

  6. Fisher ML (1981) The Lagrangean relaxation method for solving integer programs. Managem Sci 27:1–18

    MATH  Google Scholar 

  7. Geoffrion AM (1974) Lagrangean relaxation for integer programming. Math Program Stud 2:82–114

    MathSciNet  Google Scholar 

  8. Giles FR, Pulleyblank WR (1979) Total dual integrality and integer polyhedra. Linear Alg Appl 25:191–196

    Article  MathSciNet  MATH  Google Scholar 

  9. Glover F (1968) Surrogate constraints. Oper Res 16:741–749

    MathSciNet  MATH  Google Scholar 

  10. Glover F (1975) Surrogate constraint duality in mathematical programming. Oper Res 23:434–451

    MathSciNet  MATH  Google Scholar 

  11. Greenberg H, Pierskalla WP (1970) Surrogate mathematical programming. Oper Res 18:924–939

    MathSciNet  MATH  Google Scholar 

  12. Hooker JN (1992) Generalized resolution for 0–1 linear inequalities. Ann Math Artificial Intelligence 6:271–286

    Article  MathSciNet  MATH  Google Scholar 

  13. Hooker JN (1996) Inference duality as a basis for sensitivity analysis. In: Freuder EC (ed) Principles and Practice of Constraint Programming-CP96. no. 1118 of Lecture Notes Computer Sci. Springer, Berlin, pp 224–236

    Google Scholar 

  14. Jeroslow RG (1978) Cutting plane theory: Algebraic methods. Discret Math 23:121–150

    Article  MathSciNet  MATH  Google Scholar 

  15. Johnson EL (1973) Cyclic groups, cutting planes and shortest paths. In: Hu TC, Robinson S (eds) Mathematical Programming. Acad. Press, New York, pp 185–211

    Google Scholar 

  16. Karwan MH, Rardin RL (1979) Some relationships between Lagrangean & surrogate duality in integer programming. Math Program 17:320–334

    Article  MathSciNet  MATH  Google Scholar 

  17. Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York

    MATH  Google Scholar 

  18. Schrage L, Wolsey LA (1985) Sensitivity analysis for branch and bound integer programming. Oper Res 33:1008–1023

    MathSciNet  MATH  Google Scholar 

  19. Schrijver A (1986) Theory of linear and integer programming. Wiley, New York

    MATH  Google Scholar 

  20. Tind J, Wolsey LA (1981) An elementary survey of general duality theory in mathematical programming. Math Program 21

    Google Scholar 

  21. Williams HP (1984) A duality theorem for linear congruences. Discrete Appl Math 7:93–103

    Article  MathSciNet  MATH  Google Scholar 

  22. Williams HP (1996) Duality in mathematics and linear and integer programming. J Optim Th Appl 90:257–278

    Article  MATH  Google Scholar 

  23. Wolsey LA (1981) The b-hull of an integer program. Discrete Appl Math 3:193–201

    Article  MathSciNet  MATH  Google Scholar 

  24. Wolsey LA (1981) Integer programming duality: Price functions and sensitivity analysis. Math Program 20:173–195

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate School of Industrial Admin., Carnegie Mellon University, Pittsburgh, USA

    J. N. Hooker

Authors
  1. J. N. Hooker
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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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Hooker, J.N. (2008). Integer Programming Duality . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_289

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