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Duality in linear programming: From trichotomy to quadrichotomy
1. | School of Mathematical & Geospatial Sciences, RMIT University, Melbourne |
References:
[1] |
M. C. Ferris, O. L. Mangasarian and S. J. Wright, "Linear Programming with MATLAB," MPS-SIAM Series on Optimization, 7, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, Mathemathical Programming, Society (MPS), Philadelphia, PA, 2007.
doi: 10.1137/1.9780898718775. |
[2] |
H. J. Greenberg, How to analyze the results of linear programs--part 3: Infeasibility diagnosis, Interface, 23 (1993), 120-139.
doi: 10.1287/inte.23.6.120. |
[3] |
C. Li, X. He, B. Chen, Z. Gong, B. Chen and Q. Zhang, Infeasibility diagnosis on the linear programming model of production planning in refinery, Chinese J. Chem. Eng., 14 (2006), 569-573.
doi: 10.1016/S1004-9541(06)60117-1. |
[4] |
Y. Liu, An exterior point linear programming method based on inclusive normal cones, Journal of Industrial and Management Optimization, 6 (2010), 825-846.
doi: 10.3934/jimo.2010.6.825. |
[5] |
D. G. Luenburg and Y. Ye, "Linear and Nonlinear Programming," 3rd edition, International Series in Operations Research & Management Science, 116, Springer, New York, 2008. |
[6] |
G. Roodman, Post-infeasibility analysis in linear programming, Management Science, 25 (1979), 916-922.
doi: 10.1287/mnsc.25.9.916. |
show all references
References:
[1] |
M. C. Ferris, O. L. Mangasarian and S. J. Wright, "Linear Programming with MATLAB," MPS-SIAM Series on Optimization, 7, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, Mathemathical Programming, Society (MPS), Philadelphia, PA, 2007.
doi: 10.1137/1.9780898718775. |
[2] |
H. J. Greenberg, How to analyze the results of linear programs--part 3: Infeasibility diagnosis, Interface, 23 (1993), 120-139.
doi: 10.1287/inte.23.6.120. |
[3] |
C. Li, X. He, B. Chen, Z. Gong, B. Chen and Q. Zhang, Infeasibility diagnosis on the linear programming model of production planning in refinery, Chinese J. Chem. Eng., 14 (2006), 569-573.
doi: 10.1016/S1004-9541(06)60117-1. |
[4] |
Y. Liu, An exterior point linear programming method based on inclusive normal cones, Journal of Industrial and Management Optimization, 6 (2010), 825-846.
doi: 10.3934/jimo.2010.6.825. |
[5] |
D. G. Luenburg and Y. Ye, "Linear and Nonlinear Programming," 3rd edition, International Series in Operations Research & Management Science, 116, Springer, New York, 2008. |
[6] |
G. Roodman, Post-infeasibility analysis in linear programming, Management Science, 25 (1979), 916-922.
doi: 10.1287/mnsc.25.9.916. |
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