In this work 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.
A nonmonotone semismooth inexact Newton method / Bonettini, S.; Tinti, F.. - In: OPTIMIZATION METHODS & SOFTWARE. - ISSN 1055-6788. - 22:4(2007), pp. 637-657. [10.1080/10556780601079258]
A nonmonotone semismooth inexact Newton method
Bonettini S.
;
2007
Abstract
In this work 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.
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