Globally convergent Newton methods for nonsmooth equations
Mathematics of Operations Research
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Global convergence of damped Newton's method for nonsmooth equations via the path search
Mathematics of Operations Research
Approximate Newton methods for nonsmooth equations
Journal of Optimization Theory and Applications
New version of the Newton method for nonsmooth equations
Journal of Optimization Theory and Applications
Globally convergent inexact generalized Newton's methods for nonsmooth equations
Journal of Computational and Applied Mathematics
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
SIAM Journal on Numerical Analysis
Semismooth Newton Methods for Operator Equations in Function Spaces
SIAM Journal on Optimization
Computational Theory of Iterative Methods, Volume 15
Computational Theory of Iterative Methods, Volume 15
Journal of Computational and Applied Mathematics
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We provide a semilocal convergence analysis for certain modified Newton methods for solving equations containing a non-differentiable term. The sufficient convergence conditions of the corresponding Newton methods are often taken as the sufficient conditions for the modified Newton methods. That is why the latter methods are not usually treated separately from the former. However, here we show that weaker conditions, as well as a finer error analysis than before can be obtained for the convergence of modified Newton methods. Numerical examples are also provided.