A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
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
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
Inexact Newton methods for solving nonsmooth equations
Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Computational Optimization and Applications
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Methods for Solving Systems of Nonlinear Equations
Methods for Solving Systems of Nonlinear Equations
Practical implementation of an interior point nonmonotone line search filter method
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Non-negatively constrained image deblurring with an inexact interior point method
Journal of Computational and Applied Mathematics
Convergence of an inexact generalized Newton method with a scaled residual control
Computers & Mathematics with Applications
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In this article, we propose a variant of the inexact Newton method for the solution of semismooth nonlinear systems of equations. We introduce a nonmonotone scheme, which couples the inexact features with the nonmonotone strategies. For the nonmonotone scheme, we present the convergence theorems. Finally, we show how we can apply these strategies in the variational inequalities context and we present some numerical examples.