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Goldfarb, D.

On the Bartels-Golub decomposition for linear programming bases. (English) Zbl 0379.90070

Math. Program. 13, 272-279 (1977).
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Cited in 10 Documents

MSC:

90C05 Linear programming

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\textit{D. Goldfarb}, Math. Program. 13, 272--279 (1977; Zbl 0379.90070)
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References:

[1] R.H. Bartels, ”A stabilization of the simplex method”,Numerische Mathematik 16 (1971) 414–434. · Zbl 0197.43305
[2] R.H. Bartels and G.H. Golub, ”The Simplex method for linear programming using LU decomposition”,Communications of the ACM 12 (1969) 266–268. · Zbl 0181.19104
[3] J.J.H. Forrest and J.A. Tomlin, ”Updating triangular factors of the basis to maintain sparsity in the product-form Simplex method”,Mathematical Programming 2 (1972) 263–278. · Zbl 0288.90048
[4] D. Goldfarb and J.K. Reid, ”A practicable steepest edge Simplex Algorithm”, Mathematical Programming 12 (1977) 361–371. · Zbl 0443.90058
[5] D. Goldfarb, ”Using the steepest edge simplex algorithm to solve sparse linear programs”, in: J. Bunch and D. Rose, eds.,Sparse matrix computations. (Academic Press, New York, 1976) pp. 227–240. · Zbl 0345.65033
[6] P.M.J. Harris, ”Pivoting selection methods of the Devex LP code”,Mathematical Programming 5 (1973) 1–28. · Zbl 0261.90031
[7] J.K. Reid, ”A sparsity-exploiting variant of the Bartels–Golub decomposition for linear programming bases”, Harwell Rept. CCS 20, AERE Harwell (August 1975).
[8] M.A. Saunders, ”The complexity of LU updating in the Simplex method”, in: R.S. Anderssen and R.P. Brent, eds.,The complexity of computational problem solving (Queensland University Press, Queensland, 1976) pp. 214–230.
[9] J.A. Tomlin, ”On pricing and backward transformation in linear programming”,Mathematical Programming 6 (1974) 42–47. · Zbl 0278.90043
[10] P. Wolfe, ”The composite simplex algorithm”,SIAM Review 7 (1965) 42–54. · Zbl 0133.42703
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