zbMATH — the first resource for mathematics

An algorithm for determining redundant inequalities and all solutions to convex polyhedra. (English) Zbl 0288.65041

65K05 Numerical mathematical programming methods
Full Text: DOI EuDML
[1] Balinski, M. L.: An algorithm for finding all vertices of convex polyhedral sets. J. Soc. Indust. Appl. Math.9, 72-88 (1961) · Zbl 0108.33203 · doi:10.1137/0109008
[2] Chand, D. R., Kapur, S. S.: An algorithm for convex polytopes. J. Assoc. Comp. Mach.17, 78-86 (1970) · Zbl 0199.50902
[3] Chernikova, N. V.: Algorithm for finding a general formula for the nonnegative solutions of a system of linear inequalities. USSR Computational Mathematics and Mathematical Physics V, No. 2, 228-233 (1965) · Zbl 0171.35701 · doi:10.1016/0041-5553(65)90045-5
[4] Manas, M.: Methods for finding all vertices of a convex polyhedron. [Czech.] Ekonom.-Mat. Obzor5, 325-342 (1969)
[5] Manas, M., Nedoma, J.: Finding all vertices of a convex polyhedron. Num. Math.12, 226-229 (1968) · Zbl 0165.51801 · doi:10.1007/BF02162916
[6] Mattheiss, T. H.: An algorithm for determining irrelevant constraints and all vertices in systems of linear inequalities. Op. Res.21, 247-260 (1973) · Zbl 0265.90024 · doi:10.1287/opre.21.1.247
[7] Minkowski, H.: Geometrie der Zahlen, first printing 1896; reprinted by Chelsea Pub. Co., New York, 1953 · Zbl 0050.04807
[8] Motzkin, T. S., Raiffa, H., Thompson, G. L., Thrall, R. M.: The double description method. In: Contributions to the theory of games, Kuhn, H. W., Tucker, A. W. (editors). Annals of Mathematics Studies, No. 28, pp. 51-73. Princeton: Princeton University Press 1953 · Zbl 0050.14201
[9] Murty, K. G.: Solving the fixed charge problem by ranking the extreme points. Op. Res.16, 268-279 (1968) · Zbl 0249.90041 · doi:10.1287/opre.16.2.268
[10] Ya Remez, E., Shteinberg, A. S.: On a theorem on convex polyhedra in relation to the problem of finding the set of solutions of a system of linear inequalities. [Russian.]. Ukrainskii Matematicheskii Zhurnal19, 74-89 (1967)
[11] Shefi, A.: Reduction of linear inequality constraints and determination of all feasible extreme points. Ph. D. Thesis, Stanford Univ., June 1968
[12] Simonnard, M.: Linear programming. Englewood Cliffs, N. J.: Prentice Hall, Inc. 1966 · Zbl 0154.19506
[13] Stokes, R. W.: A geometric theory of solution of linear inequalities. Trans. Amer. Math. Soc.33, 782-805 (1931) · Zbl 0002.24802 · doi:10.1090/S0002-9947-1931-1501616-2
[14] Thompson, G. L., Tonge, F. M., Zionts, S.: Techniques for removing nonbinding constraints and extraneous variables from linear programming problems. Man. Sci.12, 588-608 (1965) · Zbl 0135.19904
[15] Uzawa, H.: A theorem on convex polyhedral cones. In: Studies in linear and non-linear programming, Arrow, K. J., Hurwicz, L., Uzawa, H. (editors). Stanford: Stanford Univ. Press 1958 · Zbl 0091.16002
[16] Weyl, H.: Elementare Theorie der Convexen Polyeder. Commentarii Mathematica Helvetici7, 290-306 (1935); English trans. in: Contributions to the theory of games, Kuhn, H. W., Tucker, A. W. (editors). Annals of Mathematics Studies No. 24. Princeton: Princeton Univ. Press 1950 · Zbl 0011.41104 · doi:10.1007/BF01292722
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.