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MINLP: Generalized Cross Decomposition

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Encyclopedia of Optimization

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Keywords

The Problem

The Primal Master Problem

The Dual Master Problem

The Subproblems

The Cross Decomposition Algorithm

The Convergence Tests

See also

References

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References

  1. Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Math 4:238–252

    Article  MathSciNet  MATH  Google Scholar 

  2. Dantzig GB (1963) Linear programming and extensions. Princeton Univ. Press, Princeton

    MATH  Google Scholar 

  3. Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8:101–111

    Article  MATH  Google Scholar 

  4. Floudas CA (1995) Nonlinear and mixed-integer optimization: Fundamentals and applications. Oxford Univ. Press, Oxford

    MATH  Google Scholar 

  5. Geoffrion AM (1972) Generalized Benders decomposition. J Optim Th Appl 10:237–260

    Article  MathSciNet  MATH  Google Scholar 

  6. Holmberg K (1985) Decomposition in large scale mathematical programming. PhD Thesis Dept. Math. Linköping Univ.

    Google Scholar 

  7. Holmberg K (1990) On the convergence of cross decomposition. Math Program 47:269–296

    Article  MathSciNet  MATH  Google Scholar 

  8. Holmberg K (1992) Generalized cross decomposition applied to nonlinear integer programming problems: Duality gaps and convexification in parts. Optim 23:341–356

    Article  MathSciNet  MATH  Google Scholar 

  9. Holmberg K (1994) Cross decomposition applied to integer programming problems: Duality gaps and convexification in parts. Oper Res 42(4):657–668

    Article  MathSciNet  MATH  Google Scholar 

  10. Holmberg K, Jörnsten K (1984) Cross decomposition applied to the stochastic transportation problem. Europ J Oper Res 17:361–368

    Article  MATH  Google Scholar 

  11. Van Roy TJ (1983) Cross decomposition for mixed integer programming. Math Program 25:46–63

    Article  MathSciNet  MATH  Google Scholar 

  12. Van Roy TJ (1986) A cross decomposition algorithm for capacitated facility location. Oper Res 34:145–163

    Article  MathSciNet  MATH  Google Scholar 

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© 2008 Springer-Verlag

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Holmberg, K. (2008). MINLP: Generalized Cross Decomposition . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_380

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