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Mathematical Programming at Oberwolfach pp 112–142Cite as

Characterization of facets for multiple right-hand choice linear programs

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Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 14))

Abstract

A dual or polar set is studied to characterize facets of polyhedra arising from problems in which the variables y are allowed to be continuous but the vector Wy is required to be equal to one of a finite set S. These facets are supported functions of a polar set C *, and some properties are given for those C * corresponding to a facet.

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References

  1. J. Araoz, “Polyhedral neopolarities”, Ph.D. Thesis, Faculty of Mathematics, Dept. of Computer Sciences and Applied Analysis, University of Waterloo, Waterloo, Ontario (December, 1973).

    Google Scholar 

  2. E. Balas, “Intersection cuts—A new type of cutting planes for integer programming”, Operations Research 19 (1971) 19–39.

    Article  MATH  MathSciNet  Google Scholar 

  3. C.-A. Burdet, “On the algebra and geometry of integer programming cuts”, Carnegie Mellon Management Sciences Research Rept. No. 291 (October, 1972).

    Google Scholar 

  4. G.B. Dantzig. Linear programming and extensions (Princeton University Press, Princeton, NJ 1963).

    MATH  Google Scholar 

  5. D.R. Fulkerson, “Blocking polyhedra”, in B. Harris, ed., Graph theory and its applications (Academic Press, New York, 1970).

    Google Scholar 

  6. F. Glover, “Cut search methods in integer programming”, Mathematical Programming 3 (1972) 86–100.

    Article  MATH  MathSciNet  Google Scholar 

  7. A.J. Goldman and A.W. Tucker, “Polyhedral convex cones”, in: H.W. Kuhn and A.W. Tucker, eds., Linear inequalities and related systems (Princeton University Press, Princeton, NJ, 1956).

    Google Scholar 

  8. R.E. Gomory and E.L. Johnson, “Some continuous functions related to corner polyhedra”, Mathematical Programming 3 (1972) 23–85 and 359–389.

    Article  MATH  MathSciNet  Google Scholar 

  9. R.G. Jeroslow, “The principles of cutting plane theory, Part II, Algebraic methods, disjunctive methods”, Management Science Rept. No. 371 (revised), Carnegie Mellon University (September, 1975).

    Google Scholar 

  10. E.L. Johnson, “Cyclic groups, cutting planes, and shortest paths”, in: T.C. Hu and S.M. Robinson, eds., Mathematical programming (Academic Press, New York, 1973) pp. 85–211.

    Google Scholar 

  11. E.L. Johnson, “On the group problem for mixed integer programming”, Mathematical Programming Study 2 (1974) 137–179.

    Google Scholar 

  12. E.L. Johnson, “Integer programs with continuous variables”, presented at a Workshop on Integer Programming, Bonn, West Germany, July 1974 and available as Rept. No. 7418, Institut für Operations Research, Bonn.

    Google Scholar 

  13. E.L. Johnson, “Faces of polyhedra of mixed integer programming problems”, in: Instituto Nazionale di Alta Matematica, Symposia Matematica—Volume XIX (Academic Press Inc., London, 1976) pp. 289–299.

    Google Scholar 

  14. R.T. Rockafellar, Convex analysis (Princeton University Press, Princeton, NJ, 1970).

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, New York, U.S.A.

    Ellis L. Johnson

  2. Institut für Operations Research, Universität Bonn, West Germany

    Ellis L. Johnson

Authors
  1. Ellis L. Johnson
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Editor information

H. König B. Korte K. Ritter

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© 1981 The Mathematical Programming Society

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Johnson, E.L. (1981). Characterization of facets for multiple right-hand choice linear programs. In: König, H., Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach. Mathematical Programming Studies, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120925

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  • DOI: https://doi.org/10.1007/BFb0120925

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00805-4

  • Online ISBN: 978-3-642-00806-1

  • eBook Packages: Springer Book Archive

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