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On the global convergence of a parameter-adjusting Levenberg-Marquardt method
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China, China |
References:
[1] |
J. Fan, The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence, Math. Comp., 81 (2012), 447-466.
doi: 10.1090/S0025-5718-2011-02496-8. |
[2] |
J. Fan, Accelerating the modified Levenberg-Marquardt method for nonlinear equations, Math. Comp., 83 (2014), 1173-1187.
doi: 10.1090/S0025-5718-2013-02752-4. |
[3] |
J. Fan and J. Pan, Convergence properties of a self-adaptive Levenberg-Marquardt algorithm under local error bound condition, Comput. Optim. Appl., 34 (2006), 47-62.
doi: 10.1007/s10589-005-3074-z. |
[4] |
J. Fan and Y. 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. |
[5] |
K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math., 2 (1944), 164-166. |
[6] |
D. W. Marquardt, An algorithm for least-squares estimation of nonlinear inequalities, SIAM J. Appl. Math., 11 (1963), 431-441. |
[7] |
J. J. Moré, Recent developments in algorithms and software for trust region methods, in Mathematical Programming: the state of the art (Bonn, 1982), Springer, Berlin, (1983), 258-287. |
[8] |
J. J. Moré, B. S. Garbow and K. E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software, 7 (1981), 17-41.
doi: 10.1145/355934.355936. |
[9] |
J. Nocedal and S. J. Wright, Numerical optimization, 2nd edition, Springer Series in Operations Research and Financial Engineering, Springer, New York, 2006. |
[10] |
N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method, in Topics in numerical analysis, Comput. Suppl., Springer, Vienna, 15 (2001), 239-249.
doi: 10.1007/978-3-7091-6217-0_18. |
show all references
References:
[1] |
J. Fan, The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence, Math. Comp., 81 (2012), 447-466.
doi: 10.1090/S0025-5718-2011-02496-8. |
[2] |
J. Fan, Accelerating the modified Levenberg-Marquardt method for nonlinear equations, Math. Comp., 83 (2014), 1173-1187.
doi: 10.1090/S0025-5718-2013-02752-4. |
[3] |
J. Fan and J. Pan, Convergence properties of a self-adaptive Levenberg-Marquardt algorithm under local error bound condition, Comput. Optim. Appl., 34 (2006), 47-62.
doi: 10.1007/s10589-005-3074-z. |
[4] |
J. Fan and Y. 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. |
[5] |
K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math., 2 (1944), 164-166. |
[6] |
D. W. Marquardt, An algorithm for least-squares estimation of nonlinear inequalities, SIAM J. Appl. Math., 11 (1963), 431-441. |
[7] |
J. J. Moré, Recent developments in algorithms and software for trust region methods, in Mathematical Programming: the state of the art (Bonn, 1982), Springer, Berlin, (1983), 258-287. |
[8] |
J. J. Moré, B. S. Garbow and K. E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software, 7 (1981), 17-41.
doi: 10.1145/355934.355936. |
[9] |
J. Nocedal and S. J. Wright, Numerical optimization, 2nd edition, Springer Series in Operations Research and Financial Engineering, Springer, New York, 2006. |
[10] |
N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method, in Topics in numerical analysis, Comput. Suppl., Springer, Vienna, 15 (2001), 239-249.
doi: 10.1007/978-3-7091-6217-0_18. |
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