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**Semilocal convergence analysis for inexact Newton method under weak condition.**
*(English)*
Zbl 1246.90146

Summary: Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions and \(\gamma\)-Conditions are provided and some well-known convergence theorems for Newton’s method are obtained as corollaries.

### MSC:

90C30 | Nonlinear programming |

65K05 | Numerical mathematical programming methods |

65H10 | Numerical computation of solutions to systems of equations |

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\textit{X. Xu} et al., Abstr. Appl. Anal. 2012, Article ID 982925, 13 p. (2012; Zbl 1246.90146)

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### References:

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