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A quasi-Newton trust region method based on a new fractional model
1. | Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China |
2. | Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China |
References:
[1] |
W. C. Davidon, Conic approximations and collinear scalings for optimizers,, \emph{SIAM Journal on Numerical Analysis}, 17 (1980), 268.
doi: 10.1137/0717023. |
[2] |
S. Di and W. Y. Sun, A trust region method for conic model to solve unconstraind optimizaions,, \emph{Optimization Methods and Software}, 6 (1996), 237.
doi: 10.1080/10556789608805637. |
[3] |
D. M. Gay, Computing optimal locally constrained steps,, \emph{SIAM Journal on Scientific and Statistical Computing}, 2 (1981), 186.
doi: 10.1137/0902016. |
[4] |
H. Gourgeon and J. Nocedal, A conic algorithm for optimization,, \emph{SIAM Journal on Scientific and Statistical Computing}, 6 (1985), 253.
doi: 10.1137/0906019. |
[5] |
X. P. Lu, Q. Ni and H. Liu, A dogleg method for solving new trust region subproblems of conic model,, \emph{ACTA Mathematicae Applicatae Sinica}, 30 (2009), 855. Google Scholar |
[6] |
X. P. Lu and Q. Ni, A quasi-newton trust region method with a new conic model for the unconstrained optimization,, \emph{Applied Mathematics and Computation}, 204 (2008), 373.
doi: 10.1016/j.amc.2008.06.062. |
[7] |
J. J. More, B. S. Garbow and K. E. Hillstrom, Testing unconstrained optimization software,, \emph{ACM Trans. Math. Software}, 7 (1981), 17.
doi: 10.1145/355934.355936. |
[8] |
Q. Ni, Optimality conditions for trust-region subproblems involving a conic model,, \emph{SIAM Journal on Optimization}, 15 (2005), 826.
doi: 10.1137/S1052623402418991. |
[9] |
Q. Ni, Optimization Method and Program Design,, Science Press, (2009). Google Scholar |
[10] |
J. M. Peng and Y. X. Yuan, Optimality conditions for the minimization of a quadratic with two quadratic constraints,, \emph{SIAM Journal on Optimization}, 7 (1997), 579.
doi: 10.1137/S1052623494261520. |
[11] |
M. J. D. Powell, Convergence properties of a class of minimization algorithms,, in \emph{Nonlinear Programming 2}, (1975), 1.
|
[12] |
M. J. D. Powell and Y. X. Yuan, A trust region algorithm for equality constrained optimization,, \emph{Mathematical Programming}, 49 (1990), 189.
doi: 10.1007/BF01588787. |
[13] |
R. Schnabel, Conic methods for unconstrained minimization and tensor methods for nonlinear equations,, In \emph{Mathematical Programming: The State of the Art}, (1982), 417.
|
[14] |
D. C. Sorensen, Newton's method with a model trust region modification,, \emph{SIAM Journal on Numerical Analysis}, 19 (1982), 409.
doi: 10.1137/0719026. |
[15] |
W. Y. Sun and Y. X. Yuan, A conic trust-region method for nonlinearly constrained optimization,, \emph{Annals of Operations Research}, 103 (2001), 175.
doi: 10.1023/A:1012955122229. |
[16] |
F. S. Wang, K. C. Zhang, C. L. Wang and L. Wang, A variant of trust-region methods for unconstrained optimization,, \emph{Applied Mathematics and Computation}, 203 (2008), 297.
doi: 10.1016/j.amc.2008.04.049. |
[17] |
J. Y. Wang and Q. Ni, An algorithm for solving new trust region subproblem with conic model,, \emph{Science in China, 51 (2008), 461.
doi: 10.1007/s11425-007-0149-6. |
[18] |
H. P. Wu and Q. Ni, A new trust region algorithm with conic model,, \emph{Numerical Mathematics: A Journal of Chinese Universities}, 30 (2008), 57.
|
[19] |
C. X. Xu and X. Y. Yang, Convergence of conic quasi-Newton trust region methods for unconstrained minimization,, \emph{Mathematical Application}, 11 (1998), 71.
|
[20] |
Y. X. Yuan, A review of trust region algorithms for optimization,, \emph{ICIAM}, 99 (2000), 271.
|
[21] |
L. W. Zhang and Q. Ni, Trust region algorithm of new conic model for nonliearly equality constrained optimization,, \emph{Journal on Numerical Methods and Computer Applications}, 31 (2010), 279.
|
[22] |
X. Zhang, J. Wen and Q. Ni, Subspace trust-region algorithm with conic model for unconstrained optimization,, \emph{Numerical Algebra, 3 (2013), 223.
doi: 10.3934/naco.2013.3.223. |
[23] |
L. J. Zhao and W. Y. Sun, Nonmonotone retrospective conic trust region method for unconstrained optimization,, \emph{Numerical Algebra, 3 (2013), 309.
doi: 10.3934/naco.2013.3.309. |
[24] |
X. Zhao and X. Y. Wang, A nonmonotone self-adaptive search based on trust region algorithm with line the new conic model,, \emph{Journal of Taiyuan University of Science and Technology}, 31 (2010), 68. Google Scholar |
[25] |
M. F. Zhu, Y. Xue and F. S. Zhang, A quasi-Newton type trust region method based on the conic model,, \emph{Numerical Mathematics A Journal of Chinese Universities, 17 (1995), 36.
|
show all references
References:
[1] |
W. C. Davidon, Conic approximations and collinear scalings for optimizers,, \emph{SIAM Journal on Numerical Analysis}, 17 (1980), 268.
doi: 10.1137/0717023. |
[2] |
S. Di and W. Y. Sun, A trust region method for conic model to solve unconstraind optimizaions,, \emph{Optimization Methods and Software}, 6 (1996), 237.
doi: 10.1080/10556789608805637. |
[3] |
D. M. Gay, Computing optimal locally constrained steps,, \emph{SIAM Journal on Scientific and Statistical Computing}, 2 (1981), 186.
doi: 10.1137/0902016. |
[4] |
H. Gourgeon and J. Nocedal, A conic algorithm for optimization,, \emph{SIAM Journal on Scientific and Statistical Computing}, 6 (1985), 253.
doi: 10.1137/0906019. |
[5] |
X. P. Lu, Q. Ni and H. Liu, A dogleg method for solving new trust region subproblems of conic model,, \emph{ACTA Mathematicae Applicatae Sinica}, 30 (2009), 855. Google Scholar |
[6] |
X. P. Lu and Q. Ni, A quasi-newton trust region method with a new conic model for the unconstrained optimization,, \emph{Applied Mathematics and Computation}, 204 (2008), 373.
doi: 10.1016/j.amc.2008.06.062. |
[7] |
J. J. More, B. S. Garbow and K. E. Hillstrom, Testing unconstrained optimization software,, \emph{ACM Trans. Math. Software}, 7 (1981), 17.
doi: 10.1145/355934.355936. |
[8] |
Q. Ni, Optimality conditions for trust-region subproblems involving a conic model,, \emph{SIAM Journal on Optimization}, 15 (2005), 826.
doi: 10.1137/S1052623402418991. |
[9] |
Q. Ni, Optimization Method and Program Design,, Science Press, (2009). Google Scholar |
[10] |
J. M. Peng and Y. X. Yuan, Optimality conditions for the minimization of a quadratic with two quadratic constraints,, \emph{SIAM Journal on Optimization}, 7 (1997), 579.
doi: 10.1137/S1052623494261520. |
[11] |
M. J. D. Powell, Convergence properties of a class of minimization algorithms,, in \emph{Nonlinear Programming 2}, (1975), 1.
|
[12] |
M. J. D. Powell and Y. X. Yuan, A trust region algorithm for equality constrained optimization,, \emph{Mathematical Programming}, 49 (1990), 189.
doi: 10.1007/BF01588787. |
[13] |
R. Schnabel, Conic methods for unconstrained minimization and tensor methods for nonlinear equations,, In \emph{Mathematical Programming: The State of the Art}, (1982), 417.
|
[14] |
D. C. Sorensen, Newton's method with a model trust region modification,, \emph{SIAM Journal on Numerical Analysis}, 19 (1982), 409.
doi: 10.1137/0719026. |
[15] |
W. Y. Sun and Y. X. Yuan, A conic trust-region method for nonlinearly constrained optimization,, \emph{Annals of Operations Research}, 103 (2001), 175.
doi: 10.1023/A:1012955122229. |
[16] |
F. S. Wang, K. C. Zhang, C. L. Wang and L. Wang, A variant of trust-region methods for unconstrained optimization,, \emph{Applied Mathematics and Computation}, 203 (2008), 297.
doi: 10.1016/j.amc.2008.04.049. |
[17] |
J. Y. Wang and Q. Ni, An algorithm for solving new trust region subproblem with conic model,, \emph{Science in China, 51 (2008), 461.
doi: 10.1007/s11425-007-0149-6. |
[18] |
H. P. Wu and Q. Ni, A new trust region algorithm with conic model,, \emph{Numerical Mathematics: A Journal of Chinese Universities}, 30 (2008), 57.
|
[19] |
C. X. Xu and X. Y. Yang, Convergence of conic quasi-Newton trust region methods for unconstrained minimization,, \emph{Mathematical Application}, 11 (1998), 71.
|
[20] |
Y. X. Yuan, A review of trust region algorithms for optimization,, \emph{ICIAM}, 99 (2000), 271.
|
[21] |
L. W. Zhang and Q. Ni, Trust region algorithm of new conic model for nonliearly equality constrained optimization,, \emph{Journal on Numerical Methods and Computer Applications}, 31 (2010), 279.
|
[22] |
X. Zhang, J. Wen and Q. Ni, Subspace trust-region algorithm with conic model for unconstrained optimization,, \emph{Numerical Algebra, 3 (2013), 223.
doi: 10.3934/naco.2013.3.223. |
[23] |
L. J. Zhao and W. Y. Sun, Nonmonotone retrospective conic trust region method for unconstrained optimization,, \emph{Numerical Algebra, 3 (2013), 309.
doi: 10.3934/naco.2013.3.309. |
[24] |
X. Zhao and X. Y. Wang, A nonmonotone self-adaptive search based on trust region algorithm with line the new conic model,, \emph{Journal of Taiyuan University of Science and Technology}, 31 (2010), 68. Google Scholar |
[25] |
M. F. Zhu, Y. Xue and F. S. Zhang, A quasi-Newton type trust region method based on the conic model,, \emph{Numerical Mathematics A Journal of Chinese Universities, 17 (1995), 36.
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