Least distance methods for the scheme of polytopes

B. Von Hohenbalken

doi:10.1007/bf01608995

journal article Dec 01, 1978

Least distance methods for the scheme of polytopes

B. Von Hohenbalken

Mathematical Programming Vol. 15 No. 1 pp. 1-11 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf01608995

Topics

No keywords indexed for this article. Browse by subject →

References

25

[1]

M.L. Balinski, “An algorithm for finding all vertices of convex polyhedral sets”,Journal of the Society for Industrial and Applied Mathematics 9 (1961) 72–88. 10.1137/0109008

[2]

C.A. Burdet, “Generating all faces of a polyhedron”,SIAM Journal on Applied Mathematics 26 (3) (1974) 479–489. 10.1137/0126045

[3]

A. Charnes, “Optimality and degeneracy in linear programming”,Econometrica 20 (1952) 160–170. 10.2307/1907845

[4]

An Algorithm for Convex Polytopes

Donald R. Chand, Sham S. Kapur

Journal of the ACM 1970 10.1145/321556.321564

[5]

B.L. Clarke, “Stability of the Bromate-Cerium-Malonic acid network: I Theoretical formulation, II Steady state formic acid case”,Journal of Chemical Physics 64 (10) (1976) 4165–4191. 10.1063/1.431987

[6]

M.J. Farrell and M. Fieldhouse, “Estimating efficient production functions under increasing returns to scale”,Journal of the Royal Statistical Society Ser. A 125 (II) (1962) 252–267. 10.2307/2982329

[7]

B. Gruenbaum,Convex polytopes (John Wiley, New York 1967).

[8]

G. Hadley, Linear programming (Addison Wesley, Reading, MA, 1962).

[9]

D.A. Kohler, “Projections of convex polyhedral sets”, Rept. from Operations Research Center, Univ. Calif. Berkeley (August 1967). 10.21236/ad0659301

[10]

M. Maňas, “Methods for finding all vertices of a convex polyhedron” (Czech),Ekonom.-Mat. Obzor 5 (1969) 325–342.

[11]

M. Maňas and J. Nedoma, “Finding all vertices of a convex polyhedron”,Numerische Mathematik 12 (1968) 226–229. 10.1007/bf02162916

[12]

I.H. Matheiss, “An algorithm for determining irrelevant constraints and all vertices in systems of linear inequalities”,Operations Research 21 (1973) 247–260. 10.1287/opre.21.1.247

[13]

P. McMullen and G.C. Shephard,Convex polytopes and the upper bound conjecture (Cambridge Univ. Press, London, 1971).

[14]

W.B. McRae and E.R. Davidson, “An algorithm for the extreme rays of a pointed convex polyhedral cone”, to appear.

[15]

I.S. Motzkin, H. Raiffa, G. Thompson and R. Thrall, “The double description method”, in:Contributions to the theory of games II, Ann. of Math. Studies No. 28 (Princeton Univ. Press, Princeton, NJ, 1953) pp. 51–73.

[16]

E. Ya Pemez and A.S. Shteinberg, “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 zhurnal 19 (1967) 74–89.

[17]

J.D. Pryce, “Another algorithm for computing all vertices of a convex polyhedron”, unpublished typescript (April 1969).

[18]

R. Schachtman, “Generation of the admissible boundary of a convex polytope”, Rept. from Dept. of Statistics, Univ. of North Carolina, (Feb. 1971).

[19]

G.L. Thompson, F.M. Tonge and S. Zionts, “Techniques for removing non-binding constraints and extraneous variables from linear programming problems”,Management Science 12 (1965) 588–608. 10.1287/mnsc.12.7.588

[20]

B. Von Hohenbalken, “Finding faces of polytopes by simplicial decomposition; Part I: Vertices and edges” Research Paper Series, No. 24, Dept. of Economics, Univ. of Alberta (1975).

[21]

B. Von Hohenbalken, “Finding faces of polytopes by simplicial decomposition; Part II: Higher-dimensional faces” Research Paper Series, No. 25, Dept. of Economics, Univ. of Alberta (1975).

[22]

B. Von Hohenbalken, “A finite algorithm to maximize certain pseudoconcave functions on polytopes”Mathematical Programming 8 (1975) 189–206. 10.1007/bf01681343

[23]

B. Von Hohenbalken, “Simplicial decomposition in nonlinear programming algorithms”,Mathematical Programming 13 (1977) 49–68. 10.1007/bf01584323

[24]

Algorithms for frames and lineality spaces of cones

Roger J. B. Wets, Christoph Witzgall

Journal of Research of the National Bureau of Stan... 1967 10.6028/jres.071b.001

[25]

Finding the nearest point in A polytope

Philip Wolfe

Mathematical Programming 1976 10.1007/bf01580381

Metrics

18

Citations

25

References

Details

Published: Dec 01, 1978
Vol/Issue: 15(1)
Pages: 1-11
License: View

Authors

B

B. Von Hohenbalken

Cite This Article

B. Von Hohenbalken (1978). Least distance methods for the scheme of polytopes. Mathematical Programming, 15(1), 1-11. https://doi.org/10.1007/bf01608995

Least distance methods for the scheme of polytopes

You May Also Like