Globally convergent inexact generalized Newton's methods for nonsmooth equations

Authors:
Pu Dingguo;Tian Weiwen
Affiliations:
Department of Mathematics, Tongji University, Tongji, People's Republic of China;Department of Mathematics, Shanghai University, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 5
Cited 5

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Abstract

In this paper, motivated by the Martinez and Qi methods (J. Comput. Appl. Math. 60 (1995) 127), we propose one type of globally convergent inexact generalized Newton's methods to solve nonsmooth equations in which the functions are nondifferentiable, but are Lipschitz continuous. The methods make the norm of the functions decreasing. These methods are implementable and globally convergent. We also prove that the algorithms have superlinear convergence rates under some mild conditions.