A perturbed version of an inexact generalized Newton method for solving nonsmooth equations

Authors:
Marek J. Śmietański
Affiliations:
Faculty of Mathematics and Computer Science, University of Łódź, Łódź, Poland 90-238
Venue:
Numerical Algorithms
Year:
2013

Citing 16
Cited 0

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Abstract

In this paper, we present the combination of the inexact Newton method and the generalized Newton method for solving nonsmooth equations F(x)驴=驴0, characterizing the local convergence in terms of the perturbations and residuals. We assume that both iteration matrices taken from the B-differential and vectors F(x (k)) are perturbed at each step. Some results are motivated by the approach of C驴tina驴 regarding to smooth equations. We study the conditions, which determine admissible magnitude of perturbations to preserve the convergence of method. Finally, the utility of these results is considered based on some variant of the perturbed inexact generalized Newton method for solving some general optimization problems.