zbMATH — the first resource for mathematics

The local convergence analysis of inexact quasi-Gauss-Newton method under the Hölder condition. (English) Zbl 1338.90395
Summary: In this article, we introduce the local convergence of the inexact quasi-Gauss-Newton method when the first Fréchet derivative of operator involved is Hölder condition. Furthermore, we give some results on the existence and uniqueness of the solution for a nonlinear function. Based on this study, the R-order of convergence is proved.
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
Full Text: DOI
[1] Hernandez, MA, The Newton method for operators with Hölder continuous first derivative, J. Optim. Theory Appl., 109, 631-648, (2001) · Zbl 1012.65052
[2] Wang, XH, Convergence of newton’s method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal., 20, 123-134, (2000) · Zbl 0942.65057
[3] Dembo, RS; Eisenstat, SC; Steihaug, T, Inexact Newton methods, SIAM J. Numer. Anal., 19, 400-408, (1982) · Zbl 0478.65030
[4] Ypma, TJ, Local convergence of inexact Newton methods, SIAM J. Numer. Anal., 21, 583-590, (1984) · Zbl 0566.65037
[5] Li, C; Shen, WP, Local convergence of inexact methods under the Hölder condition, J. Comput. Appl. Math., 222, 544-560, (2008) · Zbl 1181.65082
[6] Facchinei, F; Kanzow, C, A nonsmooth inexact Newton method for the solution of large scale complementarity problems, Math. Program., 76, 493-512, (1997) · Zbl 0871.90096
[7] Kanzow, C, Inexact semismooth Newton method for large-scale complementarity problems, Optim. Methods Softw., 19, 309-325, (2004) · Zbl 1141.90558
[8] Krejić, N; Martínez, JM, Inexact-Newton methods for semismooth systems of equations with block-angular structure, J. Comput. Appl. Math., 103, 239-249, (1999) · Zbl 0946.65032
[9] Martínez, JM; Qi, LQ, Inexact newton’s method for solving nonsmooth equations, J. Comput. Appl. Math., 60, 127-145, (1995) · Zbl 0833.65045
[10] Chen, JH, The convergence analysis of exact Gauss-Newton methods for nonlinear problems, J. Comput. Optim. Appl., 40, 97-118, (2008) · Zbl 1192.90200
[11] Kim, S; Tewarson, RP, The convergence of quasi-Gauss-Newton methods for nonlinear problems, Comput. Math. Appl., 29, 27-38, (1995) · Zbl 0831.65056
[12] Albeanu, G, On the convergence of the quasi-Gauss-Newton methods for solving nonlinear systems, Int. J. Comput. Math., 66, 93-99, (1998) · Zbl 0890.65047
[13] Wang, H; Tewarson, RP, A quasi-Gauss-Newton method for solving nonlinear algebraic equations, Comput. Math. Appl., 25, 53-63, (1993) · Zbl 0788.65060
[14] Kim, S, A Kantorovich-type convergence analysis for the quasi-Gauss-Newton method, J. Korean Math. Soc., 33, 865-878, (1996) · Zbl 0872.65044
[15] Morini, B, Convergence behaviour of inexact Newton methods, Math. Comput., 68, 1605-1613, (1999) · Zbl 0933.65050
[16] Stakgold, I.: Green’s Functions and Boundary-Value Problem. Wiley, New York (1998) · Zbl 0897.35001
[17] Argyros, IK, Remarks on the convergence of newton’s method under Hölder continuity conditions, Tamkang J. Math., 23, 269-277, (1992) · Zbl 0767.65051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.