Local convergence analysis of inexact Newton-like methods under majorant condition

Authors:
O. P. Ferreira;M. L. Gonçalves
Affiliations:
IME/UFG, Campus II, Goiânia, Brazil 74001-970;IME/UFG, Campus II, Goiânia, Brazil 74001-970
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant function, which relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allow us to obtain some important special cases.