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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, SIAM Journal on Numerical Analysis, 17 (1980), 268-281.
doi: 10.1137/0717023. |
[2] |
S. Di and W. Y. Sun, A trust region method for conic model to solve unconstraind optimizaions, Optimization Methods and Software, 6 (1996), 237-263.
doi: 10.1080/10556789608805637. |
[3] |
D. M. Gay, Computing optimal locally constrained steps, SIAM Journal on Scientific and Statistical Computing, 2 (1981), 186-197.
doi: 10.1137/0902016. |
[4] |
H. Gourgeon and J. Nocedal, A conic algorithm for optimization, SIAM Journal on Scientific and Statistical Computing, 6 (1985), 253-267.
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, ACTA Mathematicae Applicatae Sinica, 30 (2009), 855-871. |
[6] |
X. P. Lu and Q. Ni, A quasi-newton trust region method with a new conic model for the unconstrained optimization, Applied Mathematics and Computation, 204 (2008), 373-384.
doi: 10.1016/j.amc.2008.06.062. |
[7] |
J. J. More, B. S. Garbow and K. E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software, 7 (1981), 17-41.
doi: 10.1145/355934.355936. |
[8] |
Q. Ni, Optimality conditions for trust-region subproblems involving a conic model, SIAM Journal on Optimization, 15 (2005), 826-837.
doi: 10.1137/S1052623402418991. |
[9] |
Q. Ni, Optimization Method and Program Design, Science Press, Beijing, 2009. |
[10] |
J. M. Peng and Y. X. Yuan, Optimality conditions for the minimization of a quadratic with two quadratic constraints, SIAM Journal on Optimization, 7 (1997), 579-594.
doi: 10.1137/S1052623494261520. |
[11] |
M. J. D. Powell, Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, (eds. O.L. Mangasarian, R.R. Meyer and S.M. Robinson), Academic Press, New York, (1975), 1-27. |
[12] |
M. J. D. Powell and Y. X. Yuan, A trust region algorithm for equality constrained optimization, Mathematical Programming, 49 (1990), 189-211.
doi: 10.1007/BF01588787. |
[13] |
R. Schnabel, Conic methods for unconstrained minimization and tensor methods for nonlinear equations, In Mathematical Programming: The State of the Art, (eds. A. Bachem, M. Gr\"otschel and B. Korte), Springer-Verlag, Heidelberg, (1982), 417-438. |
[14] |
D. C. Sorensen, Newton's method with a model trust region modification, SIAM Journal on Numerical Analysis, 19 (1982), 409-426.
doi: 10.1137/0719026. |
[15] |
W. Y. Sun and Y. X. Yuan, A conic trust-region method for nonlinearly constrained optimization, Annals of Operations Research, 103 (2001), 175-191.
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, Applied Mathematics and Computation, 203 (2008), 297-307.
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, Science in China, Series A: Mathematics, 51 (2008), 461-473.
doi: 10.1007/s11425-007-0149-6. |
[18] |
H. P. Wu and Q. Ni, A new trust region algorithm with conic model, Numerical Mathematics: A Journal of Chinese Universities, 30 (2008), 57-67. |
[19] |
C. X. Xu and X. Y. Yang, Convergence of conic quasi-Newton trust region methods for unconstrained minimization, Mathematical Application, 11 (1998), 71-76. |
[20] |
Y. X. Yuan, A review of trust region algorithms for optimization, ICIAM, 99 (2000), 271-282. |
[21] |
L. W. Zhang and Q. Ni, Trust region algorithm of new conic model for nonliearly equality constrained optimization, Journal on Numerical Methods and Computer Applications, 31 (2010), 279-289. |
[22] |
X. Zhang, J. Wen and Q. Ni, Subspace trust-region algorithm with conic model for unconstrained optimization, Numerical Algebra, Control and Optimization, 3 (2013), 223-234.
doi: 10.3934/naco.2013.3.223. |
[23] |
L. J. Zhao and W. Y. Sun, Nonmonotone retrospective conic trust region method for unconstrained optimization, Numerical Algebra, Control and Optimization, 3 (2013), 309-325.
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, Journal of Taiyuan University of Science and Technology, 31 (2010), 68-71. |
[25] |
M. F. Zhu, Y. Xue and F. S. Zhang, A quasi-Newton type trust region method based on the conic model, Numerical Mathematics A Journal of Chinese Universities, 17 (1995), 36-47. |
show all references
References:
[1] |
W. C. Davidon, Conic approximations and collinear scalings for optimizers, SIAM Journal on Numerical Analysis, 17 (1980), 268-281.
doi: 10.1137/0717023. |
[2] |
S. Di and W. Y. Sun, A trust region method for conic model to solve unconstraind optimizaions, Optimization Methods and Software, 6 (1996), 237-263.
doi: 10.1080/10556789608805637. |
[3] |
D. M. Gay, Computing optimal locally constrained steps, SIAM Journal on Scientific and Statistical Computing, 2 (1981), 186-197.
doi: 10.1137/0902016. |
[4] |
H. Gourgeon and J. Nocedal, A conic algorithm for optimization, SIAM Journal on Scientific and Statistical Computing, 6 (1985), 253-267.
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, ACTA Mathematicae Applicatae Sinica, 30 (2009), 855-871. |
[6] |
X. P. Lu and Q. Ni, A quasi-newton trust region method with a new conic model for the unconstrained optimization, Applied Mathematics and Computation, 204 (2008), 373-384.
doi: 10.1016/j.amc.2008.06.062. |
[7] |
J. J. More, B. S. Garbow and K. E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software, 7 (1981), 17-41.
doi: 10.1145/355934.355936. |
[8] |
Q. Ni, Optimality conditions for trust-region subproblems involving a conic model, SIAM Journal on Optimization, 15 (2005), 826-837.
doi: 10.1137/S1052623402418991. |
[9] |
Q. Ni, Optimization Method and Program Design, Science Press, Beijing, 2009. |
[10] |
J. M. Peng and Y. X. Yuan, Optimality conditions for the minimization of a quadratic with two quadratic constraints, SIAM Journal on Optimization, 7 (1997), 579-594.
doi: 10.1137/S1052623494261520. |
[11] |
M. J. D. Powell, Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, (eds. O.L. Mangasarian, R.R. Meyer and S.M. Robinson), Academic Press, New York, (1975), 1-27. |
[12] |
M. J. D. Powell and Y. X. Yuan, A trust region algorithm for equality constrained optimization, Mathematical Programming, 49 (1990), 189-211.
doi: 10.1007/BF01588787. |
[13] |
R. Schnabel, Conic methods for unconstrained minimization and tensor methods for nonlinear equations, In Mathematical Programming: The State of the Art, (eds. A. Bachem, M. Gr\"otschel and B. Korte), Springer-Verlag, Heidelberg, (1982), 417-438. |
[14] |
D. C. Sorensen, Newton's method with a model trust region modification, SIAM Journal on Numerical Analysis, 19 (1982), 409-426.
doi: 10.1137/0719026. |
[15] |
W. Y. Sun and Y. X. Yuan, A conic trust-region method for nonlinearly constrained optimization, Annals of Operations Research, 103 (2001), 175-191.
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, Applied Mathematics and Computation, 203 (2008), 297-307.
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, Science in China, Series A: Mathematics, 51 (2008), 461-473.
doi: 10.1007/s11425-007-0149-6. |
[18] |
H. P. Wu and Q. Ni, A new trust region algorithm with conic model, Numerical Mathematics: A Journal of Chinese Universities, 30 (2008), 57-67. |
[19] |
C. X. Xu and X. Y. Yang, Convergence of conic quasi-Newton trust region methods for unconstrained minimization, Mathematical Application, 11 (1998), 71-76. |
[20] |
Y. X. Yuan, A review of trust region algorithms for optimization, ICIAM, 99 (2000), 271-282. |
[21] |
L. W. Zhang and Q. Ni, Trust region algorithm of new conic model for nonliearly equality constrained optimization, Journal on Numerical Methods and Computer Applications, 31 (2010), 279-289. |
[22] |
X. Zhang, J. Wen and Q. Ni, Subspace trust-region algorithm with conic model for unconstrained optimization, Numerical Algebra, Control and Optimization, 3 (2013), 223-234.
doi: 10.3934/naco.2013.3.223. |
[23] |
L. J. Zhao and W. Y. Sun, Nonmonotone retrospective conic trust region method for unconstrained optimization, Numerical Algebra, Control and Optimization, 3 (2013), 309-325.
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, Journal of Taiyuan University of Science and Technology, 31 (2010), 68-71. |
[25] |
M. F. Zhu, Y. Xue and F. S. Zhang, A quasi-Newton type trust region method based on the conic model, Numerical Mathematics A Journal of Chinese Universities, 17 (1995), 36-47. |
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