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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, Shanghai, 2000. |
| [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), 605-626.
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), 493-512.
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), 1223-1232.
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), 23-39.
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), 273-287.
doi: 10.1080/02331930801951256. |
| [7] |
K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math., 2 (1944), 164-166. |
| [8] |
D. W. Marquardt, An algorithm for least-squares estimation of nonlinear inequalities, SIAM J. Appl. Math., 11 (1963), 431-441.
doi: 10.1137/0111030. |
| [9] |
G. W. Stewart and J. G. Sun, "Matrix Perturbation Theory," Academic Press, San Diego, CA, 1990. |
| [10] |
N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method, Computing, (Supplement 15), (2001), 237-249. |
show all references
References:
| [1] |
Y. H. Dai and Y. X. Yuan, "Nonlinear Conjugate Gradient Methods," Shanghai Science and Technology Publisher, Shanghai, 2000. |
| [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), 605-626.
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), 493-512.
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), 1223-1232.
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), 23-39.
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), 273-287.
doi: 10.1080/02331930801951256. |
| [7] |
K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math., 2 (1944), 164-166. |
| [8] |
D. W. Marquardt, An algorithm for least-squares estimation of nonlinear inequalities, SIAM J. Appl. Math., 11 (1963), 431-441.
doi: 10.1137/0111030. |
| [9] |
G. W. Stewart and J. G. Sun, "Matrix Perturbation Theory," Academic Press, San Diego, CA, 1990. |
| [10] |
N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method, Computing, (Supplement 15), (2001), 237-249. |
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