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Robust solutions to Euclidean facility location problems with uncertain data
1. | Department of Mathematical Sciences, Tsinghua University, Beijing 100084 |
2. | Department of Mathematics, National Cheng Kung University, Tainan |
References:
[1] |
F. Alizadeh and D. Goldfarb, Second-order cone programming, Math. Programming, Ser. B, 95 (2003), 3-51. |
[2] |
M. M. Ali and L. Masinga, A nonlinear optimization model for optimal order quantities with stochastic demand rate and price change, J. Ind. Manag. Optim., 3 (2007), 139-154. |
[3] |
K. D. Andersen, E. Christiansen, A. R. Conn and M. L. Overton, An efficient primal-dual interior-point method for minimizing a sum of Euclidean norms, SIAM J. Sci. Comput., 22 (2000), 243-262.
doi: 10.1137/S1064827598343954. |
[4] |
A. Ben-Tal, A. Nemirovski and C. Roos, Robust solutions of uncertain quadratic and conic-quadratic problems, SIAM J. Optim., 13 (2002), 535-560.
doi: 10.1137/S1052623401392354. |
[5] |
A. Ben-Tal and A. Nemirovski, Robust convex optimization, Math. Oper. Res., 23 (1998), 769-805.
doi: 10.1287/moor.23.4.769. |
[6] |
L. El-Ghaoui and H. Lebret, Robust solutions to least-square problems with uncertain data matrices, SIAM J. Matrix Anal. Appl., 18 (1997), 1035-1064.
doi: 10.1137/S0895479896298130. |
[7] |
M. L. Overton, A quadratically convergent method for minimizing a sum of Euclidean norms, Math. Programming, 27 (1983), 34-63.
doi: 10.1007/BF02591963. |
[8] |
L. Qi and G. Zhou, A smoothing Newton method for minimizing a sum of Euclidean norms, SIAM J. Optim., 11 (2000), 389-410.
doi: 10.1137/S105262349834895X. |
[9] |
M. Shunko and S. Gavirneni, Role of Transfer prices in global supply chains with random demands, J. Ind. Manag. Optim., 3 (2007), 99-117. |
[10] |
G. L. Xue and Y. Ye, An efficient algorithm for minimizing a sum of $p$-norms, SIAM J. Optim., 10 (2000), 551-579.
doi: 10.1137/S1052623497327088. |
show all references
References:
[1] |
F. Alizadeh and D. Goldfarb, Second-order cone programming, Math. Programming, Ser. B, 95 (2003), 3-51. |
[2] |
M. M. Ali and L. Masinga, A nonlinear optimization model for optimal order quantities with stochastic demand rate and price change, J. Ind. Manag. Optim., 3 (2007), 139-154. |
[3] |
K. D. Andersen, E. Christiansen, A. R. Conn and M. L. Overton, An efficient primal-dual interior-point method for minimizing a sum of Euclidean norms, SIAM J. Sci. Comput., 22 (2000), 243-262.
doi: 10.1137/S1064827598343954. |
[4] |
A. Ben-Tal, A. Nemirovski and C. Roos, Robust solutions of uncertain quadratic and conic-quadratic problems, SIAM J. Optim., 13 (2002), 535-560.
doi: 10.1137/S1052623401392354. |
[5] |
A. Ben-Tal and A. Nemirovski, Robust convex optimization, Math. Oper. Res., 23 (1998), 769-805.
doi: 10.1287/moor.23.4.769. |
[6] |
L. El-Ghaoui and H. Lebret, Robust solutions to least-square problems with uncertain data matrices, SIAM J. Matrix Anal. Appl., 18 (1997), 1035-1064.
doi: 10.1137/S0895479896298130. |
[7] |
M. L. Overton, A quadratically convergent method for minimizing a sum of Euclidean norms, Math. Programming, 27 (1983), 34-63.
doi: 10.1007/BF02591963. |
[8] |
L. Qi and G. Zhou, A smoothing Newton method for minimizing a sum of Euclidean norms, SIAM J. Optim., 11 (2000), 389-410.
doi: 10.1137/S105262349834895X. |
[9] |
M. Shunko and S. Gavirneni, Role of Transfer prices in global supply chains with random demands, J. Ind. Manag. Optim., 3 (2007), 99-117. |
[10] |
G. L. Xue and Y. Ye, An efficient algorithm for minimizing a sum of $p$-norms, SIAM J. Optim., 10 (2000), 551-579.
doi: 10.1137/S1052623497327088. |
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