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Elzinga, Jack; Moore, Thomas G.

A central cutting plane algorithm for the convex programming problem. (English) Zbl 0318.90048

Math. Program. 8, 134-145 (1975).
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scan of Zbl 0318.90048

Cited in 3 Reviews
Cited in 42 Documents

MSC:

90C25 Convex programming
65K05 Numerical mathematical programming methods
49M99 Numerical methods in optimal control
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Full Text: DOI

References:

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[2] G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, N.J., 1963). · Zbl 0108.33103
[3] B.C. Eaves and W.I. Zangwill, ”Generalized cutting plane algorithms”,SIAM Journal on Control 9 (1971) 529–542. · doi:10.1137/0309037
[4] D.J. Elzinga and T.G. Moore, ”Computational experience with the central cutting plane algorithm”, in:Proceedings of ACM annual conference, Atlanta, Georgia, 1973, pp. 451–455.
[5] A.M. Geoffrion, ”Elements of large-scale mathematical programming”,Management Science 16 (1970) 652–691. · Zbl 0209.22801 · doi:10.1287/mnsc.16.11.652
[6] J.E. Kelley, Jr., ”The cutting-plane method for solving convex programs”,Journal of the Society for Industrial and Applied Mathematics 8 (1960) 703–712. · Zbl 0098.12104 · doi:10.1137/0108053
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[8] T.G. Moore, ”The central cutting plane algorithm”, unpublished Ph.D. thesis, The Johns Hopkins University (1973).
[9] G.L. Nemhauser and W.B. Widhelm, ”A modified linear program for columnar methods in mathematical programming”,Operations Research 19 (1971) 1051–1060. · Zbl 0223.90018 · doi:10.1287/opre.19.4.1051
[10] M.L. Slater, ”Lagrange multipliers revisited: a contribution to nonlinear programming”,Cowles Commission Discussion Paper, Mathematics 403 (1950).
[11] D.M. Topkis, ”Cutting plane methods without nested constraint sets”,Operations Research 18 (1970) 404–413. · Zbl 0205.21903 · doi:10.1287/opre.18.3.404
[12] D.M. Topkis, ”A note on cutting plane methods without nested constraint sets”,Operations Research 18 (1970) 1216–1220. · Zbl 0229.90043 · doi:10.1287/opre.18.6.1216
[13] A.F. Veinott, Jr., ”The supporting hyperplane method for unimodal programming”,Operations Research 15 (1967) 147–152. · Zbl 0147.38604 · doi:10.1287/opre.15.1.147
[14] P. Wolfe, ”Convergence theory in nonlinear programming”, in: J. Abadie, ed.,Integer and nonlinear programming (North-Holland, Amsterdam, 1970) pp. 1–36. · Zbl 0336.90045
[15] P. Wolfe, private communication (1974).
[16] W.I. Zangwill,Nonlinear programming: a unified approach (Prentice-Hall, Englewood Cliffs, N.J., 1969). · Zbl 0195.20804
[17] G. Zoutendijk, ”Nonlinear programming: a numerical survey”,SIAM Journal on Control 4 (1966) 194–210. · Zbl 0146.13303 · doi:10.1137/0304019
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