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A ladder method for linear semi-infinite programming
1. | School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476, Melbourne, Victoria 3001, Australia, Australia |
References:
[1] |
E. J. Anderson and A. S. Lewis, An extension of the simplex algorithm for semi-infinite linear programming,, Mathematical Programming, 44 (1989), 247.
doi: 10.1007/BF01587092. |
[2] |
B. Betrò, An accelerated central cutting plane algorithm for semi-infinite linear programming,, Mathematical Programming, 101 (2004), 479.
doi: 10.1007/s10107-003-0492-5. |
[3] |
D. den Hertog, J. Kaliski, C. Roos and T. Terlaky, A logarithmic barrier cutting plane method for convex programming,, Annals of Operations Research, 58 (1995), 69.
doi: 10.1007/BF02032162. |
[4] |
M. C. Ferris and A. B. Philpott, An interior point algorithm for semi-infinite linear programming,, Mathematical Programming, 43 (1989), 257.
doi: 10.1007/BF01582293. |
[5] |
M. A. Goberna and M. A. López, Linear Semi-infinite Optimization,, Wiley Series in Mathematical Methods in Practice, (1998).
|
[6] |
M. A. Goberna, Linear semi-infinite optimization: Recent advances,, in Continuous Optimization (eds. V. Jeyakumar and A. M. Rubinov), (2005), 3.
doi: 10.1007/0-387-26771-9_1. |
[7] |
R. Hettich, A review of numerical methods for semi-infinite optimization,, in Semi-infinite Programming and Applications (eds. A. V. Fiacco and K. O. Kortanek), (1983), 158.
doi: 10.1007/978-3-642-46477-5_11. |
[8] |
R. Hettich, An implementation of a discretization method for semi-infinite programming,, Mathematical Programming, 34 (1986), 354.
doi: 10.1007/BF01582235. |
[9] |
R. Hettich and K. O. Kortanek, Semi-infinite programming: Theory, methods, and applications,, SIAM Rev., 35 (1993), 380.
doi: 10.1137/1035089. |
[10] |
S. Ito, Y. Liu and K. L. Teo, A dual parametrization method for convex semi-infinite programming,, Ann. Oper. Res., 98 (2000), 189.
doi: 10.1023/A:1019208524259. |
[11] |
A. Kaplan and R. Tichatschke, Proximal interior point method for convex semi-infinite programming,, Optim. Methods Softw., 15 (2001), 87.
doi: 10.1080/10556780108805813. |
[12] |
Y. Liu, An exterior point method for linear programming based on inclusive normal cones,, J. Ind. Manag. Optim., 6 (2010), 825.
doi: 10.3934/jimo.2010.6.825. |
[13] |
Y. Liu, Duality theorem in linear programming: From trichotomy to quadrichotomy,, J. Ind. Manag. Optim., 7 (2011), 1003.
doi: 10.3934/jimo.2011.7.1003. |
[14] |
Y. Liu and K. L. Teo, A bridging method for global optimization,, J. Austral. Math. Soc. Ser. B, 41 (1999), 41.
doi: 10.1017/S0334270000011024. |
[15] |
Y. Liu, K. L. Teo and S. Y. Wu, A New quadratic semi-infinite programming algorithm based on dual parametrization,, J. Global Optim., 29 (2004), 401.
doi: 10.1023/B:JOGO.0000047910.80739.95. |
[16] |
R. Reemtsen, Discretization methods for the solution of semi-infinite programming problems,, J. Optim. Theory Appl., 71 (1991), 85.
doi: 10.1007/BF00940041. |
[17] |
G. A. Watson, Lagrangian methods for semi-infinite programming problems,, in Infinite Programming, (1985), 90.
doi: 10.1007/978-3-642-46564-2_8. |
[18] |
S. Y. Wu, S. C. Fang and C. J. Lin, Relaxed cutting plane method for solving linear semi-infinite programming problems,, J. Optim. Theory Appl., 99 (1998), 759.
doi: 10.1023/A:1021763419562. |
show all references
References:
[1] |
E. J. Anderson and A. S. Lewis, An extension of the simplex algorithm for semi-infinite linear programming,, Mathematical Programming, 44 (1989), 247.
doi: 10.1007/BF01587092. |
[2] |
B. Betrò, An accelerated central cutting plane algorithm for semi-infinite linear programming,, Mathematical Programming, 101 (2004), 479.
doi: 10.1007/s10107-003-0492-5. |
[3] |
D. den Hertog, J. Kaliski, C. Roos and T. Terlaky, A logarithmic barrier cutting plane method for convex programming,, Annals of Operations Research, 58 (1995), 69.
doi: 10.1007/BF02032162. |
[4] |
M. C. Ferris and A. B. Philpott, An interior point algorithm for semi-infinite linear programming,, Mathematical Programming, 43 (1989), 257.
doi: 10.1007/BF01582293. |
[5] |
M. A. Goberna and M. A. López, Linear Semi-infinite Optimization,, Wiley Series in Mathematical Methods in Practice, (1998).
|
[6] |
M. A. Goberna, Linear semi-infinite optimization: Recent advances,, in Continuous Optimization (eds. V. Jeyakumar and A. M. Rubinov), (2005), 3.
doi: 10.1007/0-387-26771-9_1. |
[7] |
R. Hettich, A review of numerical methods for semi-infinite optimization,, in Semi-infinite Programming and Applications (eds. A. V. Fiacco and K. O. Kortanek), (1983), 158.
doi: 10.1007/978-3-642-46477-5_11. |
[8] |
R. Hettich, An implementation of a discretization method for semi-infinite programming,, Mathematical Programming, 34 (1986), 354.
doi: 10.1007/BF01582235. |
[9] |
R. Hettich and K. O. Kortanek, Semi-infinite programming: Theory, methods, and applications,, SIAM Rev., 35 (1993), 380.
doi: 10.1137/1035089. |
[10] |
S. Ito, Y. Liu and K. L. Teo, A dual parametrization method for convex semi-infinite programming,, Ann. Oper. Res., 98 (2000), 189.
doi: 10.1023/A:1019208524259. |
[11] |
A. Kaplan and R. Tichatschke, Proximal interior point method for convex semi-infinite programming,, Optim. Methods Softw., 15 (2001), 87.
doi: 10.1080/10556780108805813. |
[12] |
Y. Liu, An exterior point method for linear programming based on inclusive normal cones,, J. Ind. Manag. Optim., 6 (2010), 825.
doi: 10.3934/jimo.2010.6.825. |
[13] |
Y. Liu, Duality theorem in linear programming: From trichotomy to quadrichotomy,, J. Ind. Manag. Optim., 7 (2011), 1003.
doi: 10.3934/jimo.2011.7.1003. |
[14] |
Y. Liu and K. L. Teo, A bridging method for global optimization,, J. Austral. Math. Soc. Ser. B, 41 (1999), 41.
doi: 10.1017/S0334270000011024. |
[15] |
Y. Liu, K. L. Teo and S. Y. Wu, A New quadratic semi-infinite programming algorithm based on dual parametrization,, J. Global Optim., 29 (2004), 401.
doi: 10.1023/B:JOGO.0000047910.80739.95. |
[16] |
R. Reemtsen, Discretization methods for the solution of semi-infinite programming problems,, J. Optim. Theory Appl., 71 (1991), 85.
doi: 10.1007/BF00940041. |
[17] |
G. A. Watson, Lagrangian methods for semi-infinite programming problems,, in Infinite Programming, (1985), 90.
doi: 10.1007/978-3-642-46564-2_8. |
[18] |
S. Y. Wu, S. C. Fang and C. J. Lin, Relaxed cutting plane method for solving linear semi-infinite programming problems,, J. Optim. Theory Appl., 99 (1998), 759.
doi: 10.1023/A:1021763419562. |
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