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Simplicial Pivoting Algorithms for Integer Programming

  • Reference work entry
Encyclopedia of Optimization

  • 192 Accesses

Article Outline

Keywords

Triangulations

Labelings

  Integer Labeling

  Vector Labeling

Pivoting

Noncycling Arguments

Max-Closed Sets

Unimodular Max-Closed Form Transformations

See also

References

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References

  1. Chandrasekaran R (1984) Integer programming problems for which a simple rounding type algorithm works. In: Progress in Combinatorial Optimization (Waterloo, Ont., 1982). Acad. Press, New York, pp 101–106

    Google Scholar 

  2. Chandru V, Hooker JN (1991) Extended Horn sets in propositional logic. J ACM 38(1):205–221

    Article  MathSciNet  MATH  Google Scholar 

  3. Cottle RW, Veinott AF Jr (1972) Polyhedral sets having a least element. Math Program 3:238–249

    Article  MathSciNet  MATH  Google Scholar 

  4. Dang Chuang Yin (1995) Triangulations and simplicial methods. Lecture Notes Economics and Math Systems, vol 421. Springer, Berlin

    MATH  Google Scholar 

  5. Dang Chuang Yin, Maaren H van (1998) A simplicial approach to the determination of an integral point of a simplex. Math Oper Res 23(2):403–415

    Article  MathSciNet  MATH  Google Scholar 

  6. Dang Chuang Yin, Maaren H van (1999) An arbitrary starting variable dimension algorithm for computing an integer point of a simplex. Comput Optim Appl 14(1):133–155

    Article  MathSciNet  MATH  Google Scholar 

  7. Eaves CB (1971) Computing Kakutani fixed points. SIAM J Appl Math 21:236–244

    Article  MathSciNet  MATH  Google Scholar 

  8. Forster W (1987) Computing “all” solutions of systems of polynomial equations by simplicial fixed point algorithms: The Computation And Modelling Of Economic Equilibria (Tilburg, 1985). In: Contrib Econom Anal, vol 167. North-Holland, Amsterdam, pp 39–57

    Google Scholar 

  9. Franco J (1997) Relative size of certain polynomial time solvable subclasses of satisfiability. In: Satisfiability problem: theory and applications (Piscataway, NJ, 1996). In: DIMACS 35. Amer. Math. Soc., Providence, RI, pp 211–223

    Google Scholar 

  10. Freund RM (1984) Variable dimension complexes. II. A unified approach to some combinatorial lemmas in topology. Math Oper Res 9(4):498–509

    Article  MathSciNet  MATH  Google Scholar 

  11. Glover F (1964) A bound escalation method for the solution of integer linear programs. Cahiers CERO 6:131–168

    MathSciNet  MATH  Google Scholar 

  12. Hochbaum DS, Naor J (1994) Simple and fast algorithms for linear and integer programs with two variables per inequality. SIAM J Comput 23(6):1179–1192

    Article  MathSciNet  MATH  Google Scholar 

  13. Kuhn HW (1977) Finding roots of polynomials by pivoting. In: Fixed Points: Algorithms And Applications (Proc. First Internat. Conf., Clemson Univ., Clemson, S.C., 1974). Acad. Press, New York, pp 11–39

    Google Scholar 

  14. Lagarias JC (1985) The computational complexity of simultaneous Diophantine approximation problems. SIAM J Comput 14(1):196–209

    Article  MathSciNet  MATH  Google Scholar 

  15. Maaren H van (1998) A simplicial algorithm for a tractable class of integer programs. Techn. Report Delft Univ. Technol. 98-33

    Google Scholar 

  16. Meyerson MD, Wright AH (1979) A new and constructive proof of the Borsuk–Ulam theorem. Proc Amer Math Soc 73(1):134–136

    Article  MathSciNet  MATH  Google Scholar 

  17. Pnueli A (1968) A method of truncated relaxation for integer programming. IBM Res. Paper

    Google Scholar 

  18. Scarf HE (1967) The approximation of fixed points of a continuous mapping. SIAM J Appl Math 15:1328–1343

    Article  MathSciNet  MATH  Google Scholar 

  19. Scarf HE (1967) The core of an N person game. Econometrica 35:50–69

    Article  MathSciNet  MATH  Google Scholar 

  20. Scarf HE (1973) The computation of economic equilibria. Cowles Foundation Monograph, vol 24. Yale Univ. Press, New Haven, CT, With the collaboration of Terje Hansen.

    MATH  Google Scholar 

  21. Schlipf JS, Annexstein FS, Franco JV, Swaminathan RP (1995) On finding solutions for extended Horn formulas. Inform Process Lett 54(3):133–137

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Delft University Technol., Delft, Netherlands

    Hans van Maaren

Authors
  1. Hans van Maaren
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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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Maaren, H.v. (2008). Simplicial Pivoting Algorithms for Integer Programming . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_616

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