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A differential equation method for solving box constrained variational inequality problems
On the convergence rate of the inexact Levenberg-Marquardt method
1. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 |
2. | Department of Mathematics, East China Normal University, Shanghai 200062 |
References:
[1] |
Y. H. Dai and Y. X. Yuan, "Nonlinear Conjugate Gradient Methods,", Shanghai Science and Technology Publisher, (2000). Google Scholar |
[2] |
H. Dan, N. Yamashita and M. Fukushima, Convergence properties of the inexact Levenberg-Marquardt method under local error bound,, Optimization Methods and Software, 17 (2002), 605.
doi: 10.1080/1055678021000049345. |
[3] |
F. Facchinei and C. Kanzow, A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems,, Mathematical Programming, 76 (1997), 493.
doi: 10.1007/BF02614395. |
[4] |
J. Y. Fan and J. Y. Pan, Inexact Levenberg-Marquardt method for nonlinear equations,, Discrete Continuous Dynamical System-Series B, 4 (2004), 1223.
doi: 10.3934/dcdsb.2004.4.1223. |
[5] |
J. Y. Fan and Y. X. Yuan, On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption,, Computing, 74 (2005), 23.
doi: 10.1007/s00607-004-0083-1. |
[6] |
A. Fischera, P. K. Shuklaa and M. Wang, On the inexactness level of robust Levenberg-Marquardt methods,, Optimization, 59 (2010), 273.
doi: 10.1080/02331930801951256. |
[7] |
K. Levenberg, A method for the solution of certain nonlinear problems in least squares,, Quart. Appl. Math., 2 (1944), 164. Google Scholar |
[8] |
D. W. Marquardt, An algorithm for least-squares estimation of nonlinear inequalities,, SIAM J. Appl. Math., 11 (1963), 431.
doi: 10.1137/0111030. |
[9] |
G. W. Stewart and J. G. Sun, "Matrix Perturbation Theory,", Academic Press, (1990).
|
[10] |
N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method,, Computing, 15 (2001), 237.
|
show all references
References:
[1] |
Y. H. Dai and Y. X. Yuan, "Nonlinear Conjugate Gradient Methods,", Shanghai Science and Technology Publisher, (2000). Google Scholar |
[2] |
H. Dan, N. Yamashita and M. Fukushima, Convergence properties of the inexact Levenberg-Marquardt method under local error bound,, Optimization Methods and Software, 17 (2002), 605.
doi: 10.1080/1055678021000049345. |
[3] |
F. Facchinei and C. Kanzow, A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems,, Mathematical Programming, 76 (1997), 493.
doi: 10.1007/BF02614395. |
[4] |
J. Y. Fan and J. Y. Pan, Inexact Levenberg-Marquardt method for nonlinear equations,, Discrete Continuous Dynamical System-Series B, 4 (2004), 1223.
doi: 10.3934/dcdsb.2004.4.1223. |
[5] |
J. Y. Fan and Y. X. Yuan, On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption,, Computing, 74 (2005), 23.
doi: 10.1007/s00607-004-0083-1. |
[6] |
A. Fischera, P. K. Shuklaa and M. Wang, On the inexactness level of robust Levenberg-Marquardt methods,, Optimization, 59 (2010), 273.
doi: 10.1080/02331930801951256. |
[7] |
K. Levenberg, A method for the solution of certain nonlinear problems in least squares,, Quart. Appl. Math., 2 (1944), 164. Google Scholar |
[8] |
D. W. Marquardt, An algorithm for least-squares estimation of nonlinear inequalities,, SIAM J. Appl. Math., 11 (1963), 431.
doi: 10.1137/0111030. |
[9] |
G. W. Stewart and J. G. Sun, "Matrix Perturbation Theory,", Academic Press, (1990).
|
[10] |
N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method,, Computing, 15 (2001), 237.
|
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