Abstract
A procedure for eliminating the extraneous edges of convex polyhedra found by Greenberg's method is presented and computational experience with it is reported.
References
N.V. Chernikova, “An algorithm for finding a general formula for non-negative solutions of a system of linear inequalities”,USSR Computational Mathematics and Mathematical Physics 5 (1965) 228–233.
M.E. Dyer and L.G. Proll, “Vertex enumeration in convex polyhedra: a comparative computational study”, in: T.B. Boffey, ed.,Proceedings of the CP77 combinatorial programming conference (University of Liverpool, Liverpool, 1977) pp. 23–43.
H. Greenberg, “An algorithm for determining redundant inequalities and all solutions to convex polyhedra”,Numerische Mathematik 24 (1975) 19–26.
B. Martos,Nonlinear programming: theory and methods (North-Holland, Amsterdam, 1974).
T.S. Motzkin, H. Raiffa, G.L. Thompson and R.M. Thrall, “The double description method”, in: H.W. Kuhn and A.W. Tucker, eds.,Contributions to the theory of games, Vol. 2 (Princeton University Press, Princeton, 1953).
B.F. Sherman, “A counterexample to Greenberg's algorithm for solving linear inequalities”,Numerische Mathematik 27 (1977) 491–492.
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Dyer, M.E., Proll, L.G. Eliminating extraneous edges in Greenberg's algorithm. Mathematical Programming 19, 106–110 (1980). https://doi.org/10.1007/BF01581632
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DOI: https://doi.org/10.1007/BF01581632