Abstract
The purpose of this paper is to study a generalization of the concept of blocking and antiblocking polyhedra that has been introduced by D.R. Fulkerson. The polyhedra studied by Fulkerson are restricted to the nonnegative orthant in Rm. The present generalization considers sets restricted to a cone. This leads to two polarity correspondences, which are related to the Minkowski polarity for convex sets.
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References
W. Fenchel, “Convex cones, sets and functions”, Lecture Notes, Princeton University, Princeton, N.J. (1951).
D.R. Fulkerson, “Blocking polyhedra”, in:Graph theory and its applications, Ed. B. Harris (Academic Press, New York, 1970) pp. 93–112.
D.R. Fulkerson, “Anti-blocking polyhedra”,Journal of Combinatorial Theory 12 (1972) 50–71.
D.R. Fulkerson, “Blocking and anti-blocking pairs of polyhedra”,Mathematical Programming 1 (1971) 168–194.
R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, N.J., 1970).
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This research was done while the author was a Visiting Fellow in the Department of Operations Research, Cornell University, being on leave from Institut for Operationsanalyse, University of Aarhus, Denmark. The visit to Cornell University was made possible through grants from Danmark—Amerika fondet, Otto Monsteds fond and Det Samfundsvidenskabelige Forskningsraad.
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Tind, J. Blocking and antiblocking sets. Mathematical Programming 6, 157–166 (1974). https://doi.org/10.1007/BF01580233
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DOI: https://doi.org/10.1007/BF01580233