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Extreme Rays of the Cones of Subadditive Functions

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Operations Research Proceedings 1998

Part of the book series: Operations Research Proceedings 1998 ((ORP,volume 1998))

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Summary

The extreme rays of the cones of functions defined on the set N = {0,1,…, n} and subadditive relative to the usual addition or addition modulo n + 1 are studied. A large class of extreme rays of the cone of monotone subadditive functions and all extreme rays of the cone of concave functions on N are found. Established set-theoretic relations between the cones allow to lessen the area where the search of extreme rays of the first two cones is worthwhile.

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References

  1. R.E. Gomory. Some polyhedra related to combinatorial problems. Lin. Algebra and its Applications, 2: 451–558, 1969.

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  2. R.E. Gomory, E.L. Johnson. Some continuous functions related to corner polyhedra I,II. Mathem. Programming, 3: 23–85, 359-389, 1972.

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  3. V.A. Shlyk. On the group-theoretic approach in integer linear programming. Izvestiya Akad. Nauk USSR. Technical Cybernetics, 1: 94–105, 1988 (in Russian).

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  4. V.A. Shlyk. Subadditive characterization of the facets of polyhedral sets on partial algebra. Dok-lady Acad. Nauk BSSR, 28: 980–983, 1984 (in Russian).

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© 1999 Springer-Verlag Berlin Heidelberg

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Shlyk, V.A. (1999). Extreme Rays of the Cones of Subadditive Functions. In: Kall, P., Lüthi, HJ. (eds) Operations Research Proceedings 1998. Operations Research Proceedings 1998, vol 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58409-1_14

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  • DOI: https://doi.org/10.1007/978-3-642-58409-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65381-3

  • Online ISBN: 978-3-642-58409-1

  • eBook Packages: Springer Book Archive

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