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An exterior point linear programming method based on inclusive normal cones
1. | School of Mathematical & Geospatial Sciences, RMIT University, Melbourne, Australia |
References:
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J. M. Borwein and A. S. Lewis, "Convex Analysis and Nonlinear Optimization. Theory and Examples," Second edition. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 3. Springer, New York, 2006. |
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G. B. Dantzig, Maximization of a linear function of variables subject to linear inequalities, Activity Analysis of Production and Allocation, 339-347; Cowles Commission Monograph No. 13. John Wiley & Sons, Inc., New York, N. Y.; Chapman & Hall, Ltd., London, 1951. |
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N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984), 373-395
doi: 10.1007/BF02579150. |
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L. G. Khachiyan, A polynomial algorithm in linear programming, Doklady Akademii Nauk SSSR-S, 244 (1979), 1093-1096; translated in Soviet Mathematics Doklady, 20 (1979), 191-194. |
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T. Terlaky and S. Zhang, Pivot rules for linear programming: A survey on recent theoretical developments, Annals of Operations Research, 46 (1993), 203-233
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R. J. Vanderbei, "Linear Programming - Foundations and Extensions," 3rd Ed., International Series in Operations Research & Management Science, 114, Springer, New York, 2008. |
show all references
References:
[1] |
J. M. Borwein and A. S. Lewis, "Convex Analysis and Nonlinear Optimization. Theory and Examples," Second edition. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 3. Springer, New York, 2006. |
[2] |
G. B. Dantzig, Maximization of a linear function of variables subject to linear inequalities, Activity Analysis of Production and Allocation, 339-347; Cowles Commission Monograph No. 13. John Wiley & Sons, Inc., New York, N. Y.; Chapman & Hall, Ltd., London, 1951. |
[3] |
N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984), 373-395
doi: 10.1007/BF02579150. |
[4] |
L. G. Khachiyan, A polynomial algorithm in linear programming, Doklady Akademii Nauk SSSR-S, 244 (1979), 1093-1096; translated in Soviet Mathematics Doklady, 20 (1979), 191-194. |
[5] |
T. Terlaky and S. Zhang, Pivot rules for linear programming: A survey on recent theoretical developments, Annals of Operations Research, 46 (1993), 203-233
doi: 10.1007/BF02096264. |
[6] |
R. J. Vanderbei, "Linear Programming - Foundations and Extensions," 3rd Ed., International Series in Operations Research & Management Science, 114, Springer, New York, 2008. |
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