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A numerically stable form of the simplex algorithm.(English)Zbl 0255.65029


MSC:

65K05 Numerical mathematical programming methods

Cite

References:

[1]Bartels, R. H., A Numerical Investigation of the Simplex Method, (Technical Report, No. CS 104 (1968), Computer Science Department, Stanford University: Computer Science Department, Stanford University Stanford, California) ·Zbl 0197.43305
[2]Bartels, R. H.; Golub, G. H., The Simplex Method of linear programming using LU decomposition, Comm. ACM, 12, 266-268 (1969) ·Zbl 0181.19104
[3]Beale, E. M.L., On quadratic programming, Naval Res. Log. Quart., 6, 227-243 (1959)
[4]Bennett, J. M., Triangular factors of modified matrices, Numerische Math., 7, 217-221 (1965) ·Zbl 0132.36204
[5]Dantzig, G. B., Linear Programming and Extensions (1965), Princeton University Press ·Zbl 0108.33103
[6]Gill, P. E.; Murray, W., Quasi-Newton methods for unconstrained optimization, J. Inst. Math. Appl., 9, 91-108 (1972) ·Zbl 0264.49026
[7]Gill, P. E.; Murray, W., Two methods for the Solution of Linearly Constrained and Unconstrained Optimization Problems, NPL DNAC Report No. 25 (1972) ·Zbl 0264.49026
[8]Hadley, G., Linear Programming (1962), Addison-Wesley: Addison-Wesley Reading, Mass ·Zbl 0102.36304
[9]Murray, W., An Algorithm for Finding a Local Minimum of an Indefinite Quadratic Program, NPL DNAC Report No. 1 (1971)
[10]Saunders, M. A., Large-Scale Linear Programming Using the Cholesky Factorization, (Technical Report No. CS 252 (1972), Computer Science Department, Stanford University: Computer Science Department, Stanford University Stanford, California) ·Zbl 0313.65048
[11]Saunders, M. A., Product Form of the Cholesky Factorization for Large-Scale Linear Programming, (Technical Report No. CS 301 (1972), Computer Science Department, Stanford University: Computer Science Department, Stanford University Stanford, California)
[12]Wilkinson, J. H., The Algebraic Eigenvalue Problem (1965), Oxford University Press ·Zbl 0258.65037
[13]Wolfe, P., The Simplex Method for Quadratic Programming, Econometrica, 27, 382-398 (1959) ·Zbl 0103.37603
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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