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Xu, Xiubin; Xiao, Yuan; Liu, Tao

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

Abstr. Appl. Anal. 2012, Article ID 982925, 13 p. (2012).
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.

Cited in 4 Documents

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
65H10 Numerical computation of solutions to systems of equations

Keywords:

semilocal convergence analysis; inexact Newton method
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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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