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Johnson, Ellis L.

Characterization of facets for multiple right-hand choice linear programs. (English) Zbl 0449.90070

Math. Program. Study 14, 112-142 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 9 Documents

MSC:

90C10 Integer programming
52Bxx Polytopes and polyhedra

Keywords:

facets; multiple right-hand choice linear programs; polar set; polyhedra; subadditivity; convexity; cutting planes; dual set
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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).
[2] E. Balas, ”Intersection cuts–A new type of cutting planes for integer programming”, Operations Research 19 (1971) 19–39. · Zbl 0219.90035 · doi:10.1287/opre.19.1.19
[3] C.-A. Burdet, ”On the algebra and geometry of integer programming cuts”, Carnegie Mellon Management Sciences Research Rept. No. 291 (October, 1972).
[4] G.B. Dantzig. Linear programming and extensions (Princeton University Press, Princeton, NJ 1963). · Zbl 0108.33103
[5] D.R. Fulkerson, ”Blocking polyhedra”, in B. Harris, ed., Graph theory and its applications (Academic Press, New York, 1970). · Zbl 0217.18505
[6] F. Glover, ”Cut search methods in integer programming”, Mathematical Programming 3 (1972) 86–100. · Zbl 0247.90042 · doi:10.1007/BF01584977
[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). · Zbl 0072.37504
[8] R.E. Gomory and E.L. Johnson, ”Some continuous functions related to corner polyhedra”, Mathematical Programming 3 (1972) 23–85 and 359–389. · Zbl 0246.90029 · doi:10.1007/BF01584976
[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).
[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.
[11] E.L. Johnson, ”On the group problem for mixed integer programming”, Mathematical Programming Study 2 (1974) 137–179. · doi:10.1007/BFb0120692
[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.
[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.
[14] R.T. Rockafellar, Convex analysis (Princeton University Press, Princeton, NJ, 1970). · Zbl 0193.18401
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