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On the global convergence of a parameter-adjusting Levenberg-Marquardt method
Analysis of complexity of primal-dual interior-point algorithms based on a new kernel function for linear optimization
1. | College of Mathematics and Physics, Bohai University, Jinzhou, MO 121000, China, China |
References:
[1] |
Y. Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization, SIAM Journal on Optimization, 15 (2004), 101-128.
doi: 10.1137/S1052623403423114. |
[2] |
Y. Q. Bai, J. Guo and C. Roos, A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms, Acta Mathematica Sinica English Series, 25 (2009), 2169-2178.
doi: 10.1007/s10114-009-6457-8. |
[3] |
Y. Q. Bai and C. Roos, A polynomial-time algorithm for linear optimization based on a new simple kernel function, Optimization Methods and Software, 18 (2003), 631-646.
doi: 10.1080/10556780310001639735. |
[4] |
Y. Q. Bai, M. El Ghami and C. Roos, A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (2002), 766-782.
doi: 10.1137/S1052623401398132. |
[5] |
Y. Q. Bai, C. Roos and M. El Ghami, A primal-dual interior-point method for linear optimization based on a new proximity function, Optimization Methods and Software, 17 (2002), 985-1008.
doi: 10.1080/1055678021000090024. |
[6] |
N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984), 373-395.
doi: 10.1007/BF02579150. |
[7] |
Y. Nesterov and A. Nemirovskii, Interior-point polynomial methods in convex programming, SIAM, Philadelphia, 1994.
doi: 10.1137/1.9781611970791. |
[8] |
J. M. Peng, C. Roos and T. Terlaky, A new class of polynomial primal-dual methods for linear and semidefinite programming, European Journal of Operational Research, 143 (2002), 234-256.
doi: 10.1016/S0377-2217(02)00275-8. |
[9] |
J. Renegar, A polynomial time algorithm based on Newton's method for linear programming, Mathematical Programming, 40 (1988), 59-94.
doi: 10.1007/BF01580724. |
[10] |
C. Roos and J. P. Vial, A polynomial method of approximate centers for linear programming, Mathematical Programming, 54 (1992), 295-305.
doi: 10.1007/BF01586056. |
show all references
References:
[1] |
Y. Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization, SIAM Journal on Optimization, 15 (2004), 101-128.
doi: 10.1137/S1052623403423114. |
[2] |
Y. Q. Bai, J. Guo and C. Roos, A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms, Acta Mathematica Sinica English Series, 25 (2009), 2169-2178.
doi: 10.1007/s10114-009-6457-8. |
[3] |
Y. Q. Bai and C. Roos, A polynomial-time algorithm for linear optimization based on a new simple kernel function, Optimization Methods and Software, 18 (2003), 631-646.
doi: 10.1080/10556780310001639735. |
[4] |
Y. Q. Bai, M. El Ghami and C. Roos, A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (2002), 766-782.
doi: 10.1137/S1052623401398132. |
[5] |
Y. Q. Bai, C. Roos and M. El Ghami, A primal-dual interior-point method for linear optimization based on a new proximity function, Optimization Methods and Software, 17 (2002), 985-1008.
doi: 10.1080/1055678021000090024. |
[6] |
N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984), 373-395.
doi: 10.1007/BF02579150. |
[7] |
Y. Nesterov and A. Nemirovskii, Interior-point polynomial methods in convex programming, SIAM, Philadelphia, 1994.
doi: 10.1137/1.9781611970791. |
[8] |
J. M. Peng, C. Roos and T. Terlaky, A new class of polynomial primal-dual methods for linear and semidefinite programming, European Journal of Operational Research, 143 (2002), 234-256.
doi: 10.1016/S0377-2217(02)00275-8. |
[9] |
J. Renegar, A polynomial time algorithm based on Newton's method for linear programming, Mathematical Programming, 40 (1988), 59-94.
doi: 10.1007/BF01580724. |
[10] |
C. Roos and J. P. Vial, A polynomial method of approximate centers for linear programming, Mathematical Programming, 54 (1992), 295-305.
doi: 10.1007/BF01586056. |
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