-
Previous Article
Reliability optimization of component assignment problem for a multistate network in terms of minimal cuts
- JIMO Home
- This Issue
-
Next Article
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. |
| [1] |
Haiyan Wang, Jinyan Fan. Convergence properties of inexact Levenberg-Marquardt method under Hölderian local error bound. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2265-2275. doi: 10.3934/jimo.2020068 |
| [2] |
Jinyan Fan, Jianyu Pan. Inexact Levenberg-Marquardt method for nonlinear equations. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1223-1232. doi: 10.3934/dcdsb.2004.4.1223 |
| [3] |
Liyan Qi, Xiantao Xiao, Liwei Zhang. On the global convergence of a parameter-adjusting Levenberg-Marquardt method. Numerical Algebra, Control and Optimization, 2015, 5 (1) : 25-36. doi: 10.3934/naco.2015.5.25 |
| [4] |
Jinyan Fan. On the Levenberg-Marquardt methods for convex constrained nonlinear equations. Journal of Industrial and Management Optimization, 2013, 9 (1) : 227-241. doi: 10.3934/jimo.2013.9.227 |
| [5] |
Xin-He Miao, Kai Yao, Ching-Yu Yang, Jein-Shan Chen. Levenberg-Marquardt method for absolute value equation associated with second-order cone. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 47-61. doi: 10.3934/naco.2021050 |
| [6] |
Jirui Ma, Jinyan Fan. On convergence properties of the modified trust region method under Hölderian error bound condition. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021222 |
| [7] |
Johann Baumeister, Barbara Kaltenbacher, Antonio Leitão. On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations. Inverse Problems and Imaging, 2010, 4 (3) : 335-350. doi: 10.3934/ipi.2010.4.335 |
| [8] |
Zhili Ge, Gang Qian, Deren Han. Global convergence of an inexact operator splitting method for monotone variational inequalities. Journal of Industrial and Management Optimization, 2011, 7 (4) : 1013-1026. doi: 10.3934/jimo.2011.7.1013 |
| [9] |
Hongxiu Zhong, Guoliang Chen, Xueping Guo. Semi-local convergence of the Newton-HSS method under the center Lipschitz condition. Numerical Algebra, Control and Optimization, 2019, 9 (1) : 85-99. doi: 10.3934/naco.2019007 |
| [10] |
Wen-ling Zhao, Dao-jin Song. A global error bound via the SQP method for constrained optimization problem. Journal of Industrial and Management Optimization, 2007, 3 (4) : 775-781. doi: 10.3934/jimo.2007.3.775 |
| [11] |
Jie-Wen He, Chi-Chon Lei, Chen-Yang Shi, Seak-Weng Vong. An inexact alternating direction method of multipliers for a kind of nonlinear complementarity problems. Numerical Algebra, Control and Optimization, 2021, 11 (3) : 353-362. doi: 10.3934/naco.2020030 |
| [12] |
Sanghoon Kwon, Seonhee Lim. Equidistribution with an error rate and Diophantine approximation over a local field of positive characteristic. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 169-186. doi: 10.3934/dcds.2018008 |
| [13] |
Yves Bourgault, Damien Broizat, Pierre-Emmanuel Jabin. Convergence rate for the method of moments with linear closure relations. Kinetic and Related Models, 2015, 8 (1) : 1-27. doi: 10.3934/krm.2015.8.1 |
| [14] |
Petr Knobloch. Error estimates for a nonlinear local projection stabilization of transient convection--diffusion--reaction equations. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 901-911. doi: 10.3934/dcdss.2015.8.901 |
| [15] |
Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 695-717. doi: 10.3934/dcdsb.2018203 |
| [16] |
Jiangxing Wang. Convergence analysis of an accurate and efficient method for nonlinear Maxwell's equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2429-2440. doi: 10.3934/dcdsb.2020185 |
| [17] |
Liping Zhang, Soon-Yi Wu, Shu-Cherng Fang. Convergence and error bound of a D-gap function based Newton-type algorithm for equilibrium problems. Journal of Industrial and Management Optimization, 2010, 6 (2) : 333-346. doi: 10.3934/jimo.2010.6.333 |
| [18] |
Fabio Camilli, Claudio Marchi. On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems. Networks and Heterogeneous Media, 2011, 6 (1) : 61-75. doi: 10.3934/nhm.2011.6.61 |
| [19] |
Shi Jin, Yingda Li. Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs. Kinetic and Related Models, 2019, 12 (5) : 969-993. doi: 10.3934/krm.2019037 |
| [20] |
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami. Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1285-1301. doi: 10.3934/cpaa.2012.11.1285 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]