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On some inverse singular value problems with Toeplitz-related structure
A filter successive linear programming method for nonlinear semidefinite programming problems
1. | School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, China, China |
References:
[1] |
A. Auslender and H. Ramírez, Penalty and barrier methods for convex semidefinite progranmming,, Mathematical Methods of Operations Research, 63 (2006), 195.
doi: 10.1007/s00186-005-0054-0. |
[2] |
M. S. Bazaraa and C. M. Shetty, "Nonlinear Programming Theory and Algorithms,", John Wiley & Sons, (1979).
|
[3] |
C. Chin and R. Flercher, On the global convergence of an SLP-Filter algorithm that takes EQP steps,, SIAM Journal on Optimization, 96 (2003), 161.
|
[4] |
R. Correa and H. Ramírez, A global algorithm for nonlinear semidefinite programming,, Math. Program., 15 (2004), 303.
|
[5] |
B. Fares, D. Noll and P. Apkarian, Robust control via sequential semidefinite programming,, SIAM Journal on Control and Optimization, 40 (2002), 1791.
doi: 10.1137/S0363012900373483. |
[6] |
R. Fletcher, N. I. M. Gould, S. Leyffer and A. Wächter, Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming,, SIAM J. Optim., 13 (2002), 635.
doi: 10.1137/S1052623499357258. |
[7] |
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function,, Mathematical Programming, 91 (2002), 239.
doi: 10.1007/s101070100244. |
[8] |
R. Fletcher, S. Leyffer and Ph.L. Toint, On the global convergence of an SLP-Filter Algorithm,, Numerical Analysis Report, (). Google Scholar |
[9] |
R. Fletcher, S. Leyffer and Ph.L. Toint, On the global convergence of a Filter-SQP Algorithm,, SIAM J. Optim., 13 (2002), 44.
doi: 10.1137/S105262340038081X. |
[10] |
N. I. M. Gould, C. Sainvitu and Ph. L. Toint, A filter-trust-region method for unconstraint optimization,, SIAM J. Optim., 16 (2005), 341.
doi: 10.1137/040603851. |
[11] |
C. Helmberg, Semidefinite programming for combinatorial optimization,, Technical Report ZIB-Report ZR-00-34, (2000), 00. Google Scholar |
[12] |
X. X. Huang, K. L. Teo and X. Q. Yang, Approximate augmented Lagrangian functions and nonlinear semidefinite programs,, Technical Report, (2003). Google Scholar |
[13] |
F. Jarre, An interior method for nonconvex semidefinite programs,, Optimization and Engineering, 1 (2000), 347.
doi: 10.1023/A:1011562523132. |
[14] |
C. Kanzow, C. Nagel, H. Kato and M. Fukushima, Succseeive linearization methods for nonlinear semidefinite programs,, Comput. Optim. Appl., 31 (2005), 251.
doi: 10.1007/s10589-005-3231-4. |
[15] |
C. Li and W. Sun, On filter-successive linearization methods for nonlinear semidefinite programming,, Science in China Series A, 52 (2009), 2341.
doi: 10.1007/s11425-009-0168-6. |
[16] |
W. Miao and W. Sun, A filter-trust-region method for unconstrained optimization,, Numerical Mathematics, 29 (2007), 88.
|
[17] |
W. Sun, On filter methods for optimization,, The 3rd Australia-China Optimization Workshop, (2007). Google Scholar |
[18] |
W. Sun, On filter-type methods for optimization: motivation and development,, An invited talk, (2008), 26. Google Scholar |
[19] |
W. Sun and Y. Yuan, "Optimzation Theory and Methods: Nonlinear Programming,", Springer, (2006). Google Scholar |
[20] |
M. J. Todd, Semidefinite optimization,, Numerical Mathematics, 10 (2001), 515.
|
[21] |
K. C. Toh, R. H. Tutuncu and M. J. Todd, SDPT3 version 4.0 (beta)- a MATLAB software for semidefinite-quadratic-linear programming,, updated in 17 July, (2006). Google Scholar |
[22] |
K. C. Toh, R. H. Tutuncu and M. J. Todd, On the implementation and usage of SDPT3 - a MATLAB software package for semidefinite-quadratic-linear programming version 4.0,, 17 July, (2006). Google Scholar |
[23] |
R. H. Tutuncu, K. C. Toh and M. J. Todd, Solving semidefinite-quadratic-linear programs using SDPT3,, Math. Prog., 95 (2003), 189. Google Scholar |
[24] |
H. Wolkowicz, R. Saigal and L. Vandenberghe, "Handbook of Semidefinite Programming,", Boston: Kluwer Academic Publishers, (2000).
|
[25] |
Z. Yang, W. Sun and L. Qi, On global convergence of a filter-trust-region algorithm for solving nonsmooth equations,, International Journal of Computer Mathematics, 87 (2010), 788.
|
[26] |
Y. Zhang, W. Sun and L. Qi, A nonmonotone filter Barzilai-Borwein method for optimization,, Asia-Pacific Journal of Operational Research, 27 (2010), 55.
|
show all references
References:
[1] |
A. Auslender and H. Ramírez, Penalty and barrier methods for convex semidefinite progranmming,, Mathematical Methods of Operations Research, 63 (2006), 195.
doi: 10.1007/s00186-005-0054-0. |
[2] |
M. S. Bazaraa and C. M. Shetty, "Nonlinear Programming Theory and Algorithms,", John Wiley & Sons, (1979).
|
[3] |
C. Chin and R. Flercher, On the global convergence of an SLP-Filter algorithm that takes EQP steps,, SIAM Journal on Optimization, 96 (2003), 161.
|
[4] |
R. Correa and H. Ramírez, A global algorithm for nonlinear semidefinite programming,, Math. Program., 15 (2004), 303.
|
[5] |
B. Fares, D. Noll and P. Apkarian, Robust control via sequential semidefinite programming,, SIAM Journal on Control and Optimization, 40 (2002), 1791.
doi: 10.1137/S0363012900373483. |
[6] |
R. Fletcher, N. I. M. Gould, S. Leyffer and A. Wächter, Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming,, SIAM J. Optim., 13 (2002), 635.
doi: 10.1137/S1052623499357258. |
[7] |
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function,, Mathematical Programming, 91 (2002), 239.
doi: 10.1007/s101070100244. |
[8] |
R. Fletcher, S. Leyffer and Ph.L. Toint, On the global convergence of an SLP-Filter Algorithm,, Numerical Analysis Report, (). Google Scholar |
[9] |
R. Fletcher, S. Leyffer and Ph.L. Toint, On the global convergence of a Filter-SQP Algorithm,, SIAM J. Optim., 13 (2002), 44.
doi: 10.1137/S105262340038081X. |
[10] |
N. I. M. Gould, C. Sainvitu and Ph. L. Toint, A filter-trust-region method for unconstraint optimization,, SIAM J. Optim., 16 (2005), 341.
doi: 10.1137/040603851. |
[11] |
C. Helmberg, Semidefinite programming for combinatorial optimization,, Technical Report ZIB-Report ZR-00-34, (2000), 00. Google Scholar |
[12] |
X. X. Huang, K. L. Teo and X. Q. Yang, Approximate augmented Lagrangian functions and nonlinear semidefinite programs,, Technical Report, (2003). Google Scholar |
[13] |
F. Jarre, An interior method for nonconvex semidefinite programs,, Optimization and Engineering, 1 (2000), 347.
doi: 10.1023/A:1011562523132. |
[14] |
C. Kanzow, C. Nagel, H. Kato and M. Fukushima, Succseeive linearization methods for nonlinear semidefinite programs,, Comput. Optim. Appl., 31 (2005), 251.
doi: 10.1007/s10589-005-3231-4. |
[15] |
C. Li and W. Sun, On filter-successive linearization methods for nonlinear semidefinite programming,, Science in China Series A, 52 (2009), 2341.
doi: 10.1007/s11425-009-0168-6. |
[16] |
W. Miao and W. Sun, A filter-trust-region method for unconstrained optimization,, Numerical Mathematics, 29 (2007), 88.
|
[17] |
W. Sun, On filter methods for optimization,, The 3rd Australia-China Optimization Workshop, (2007). Google Scholar |
[18] |
W. Sun, On filter-type methods for optimization: motivation and development,, An invited talk, (2008), 26. Google Scholar |
[19] |
W. Sun and Y. Yuan, "Optimzation Theory and Methods: Nonlinear Programming,", Springer, (2006). Google Scholar |
[20] |
M. J. Todd, Semidefinite optimization,, Numerical Mathematics, 10 (2001), 515.
|
[21] |
K. C. Toh, R. H. Tutuncu and M. J. Todd, SDPT3 version 4.0 (beta)- a MATLAB software for semidefinite-quadratic-linear programming,, updated in 17 July, (2006). Google Scholar |
[22] |
K. C. Toh, R. H. Tutuncu and M. J. Todd, On the implementation and usage of SDPT3 - a MATLAB software package for semidefinite-quadratic-linear programming version 4.0,, 17 July, (2006). Google Scholar |
[23] |
R. H. Tutuncu, K. C. Toh and M. J. Todd, Solving semidefinite-quadratic-linear programs using SDPT3,, Math. Prog., 95 (2003), 189. Google Scholar |
[24] |
H. Wolkowicz, R. Saigal and L. Vandenberghe, "Handbook of Semidefinite Programming,", Boston: Kluwer Academic Publishers, (2000).
|
[25] |
Z. Yang, W. Sun and L. Qi, On global convergence of a filter-trust-region algorithm for solving nonsmooth equations,, International Journal of Computer Mathematics, 87 (2010), 788.
|
[26] |
Y. Zhang, W. Sun and L. Qi, A nonmonotone filter Barzilai-Borwein method for optimization,, Asia-Pacific Journal of Operational Research, 27 (2010), 55.
|
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