Projection with a Minimal System of Inequalities

  • Egon Balas


Projection of a polyhedron involves the use of a cone whose extreme rays induce the inequalities defining the projection. These inequalities need not be facet defining. We introduce a transformation that produces a cone whose extreme rays induce facets of the projection.

projection of polyhedra combinatorial optimization facets of polyhedra 


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  1. 1.
    E. Balas, S. Ceria, and G. Cornuéjols, "A lift-and-project cutting plane algorithm for mixed 0-1 programs," Mathematical Programming, vol. 58, pp. 295-324, 1993.Google Scholar
  2. 2.
    E. Balas and W.R. Pulleyblank, "The perfectly matchable subgraph polytope of a bipartite graph," Networks, vol. 13, pp. 495-516, 1983.Google Scholar
  3. 3.
    E. Balas and W.R. Pulleyblank, "The perfectly matchable subgraph polytope of an arbitrary graph," Combinatorica, vol. 9, pp. 321-337, 1989.Google Scholar
  4. 4.
    M.O. Ball, W.G. Liu, and W.R. Pulleyblank, “Two terminal steiner tree polyhedra," Report No. 87466-OR, Institüt für Ökonometrie und Operations Research Bonn, 1987.Google Scholar
  5. 5.
    M.X. Goemans, "Polyhedral description of trees and arborescences,” in Integer Programming and Combinatorial Optimization (Proceedings of IPCO 2), E. Balas, G. Cornuéjols, and R. Kannan (Eds.), Carnegie Mellon University, 1992, pp. 1-14.Google Scholar
  6. 6.
    L. Lovász and A. Schrijver, "Cones of matrices and set-functions and 0-1 optimization," SIAM Journal on Optimization, vol. 1, pp. 166-190, 1991.Google Scholar
  7. 7.
    G.L. Nemhauser and L. Wolsey, Integer and Combinatorial Optimization, Wiley, 1988.Google Scholar
  8. 8.
    M. Queyranne and Y. Wang, "Single machine scheduling polyhedra with precedence constraints," Mathematics of Operations Research, vol. 16, pp. 1-20, 1991.Google Scholar
  9. 9.
    R.L. Rardin and L.A. Wolsey, "Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems," European Journal of Operational Research, vol. 71, pp. 95-109, 1993.Google Scholar
  10. 10.
    H. Sherali and W. Adams, "A hierarchy of relaxations between the continuous and convenx hull representations for zero-one programming problems," SIAM Journal on Discrete Mathematics, vol. 3, pp. 411-430, 1990.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Egon Balas
    • 1
  1. 1.Carnegie Mellon UniversityUSA

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