In this paper, we describe a variant of the inexact Newton method for solving nonlinear systems of equations.We define a nonmonotone inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone inexact Newton scheme, we present the convergence theorems. Finally, we show how we can apply these strategies to the inexact Newton interior-point method and we present some numerical examples.
A nonmonotone inexact Newton method / Bonettini, Silvia. - In: OPTIMIZATION METHODS & SOFTWARE. - ISSN 1055-6788. - STAMPA. - 20:4-5(2005), pp. 475-491. [10.1080/10556780500139971]
A nonmonotone inexact Newton method
BONETTINI, Silvia
2005
Abstract
In this paper, we describe a variant of the inexact Newton method for solving nonlinear systems of equations.We define a nonmonotone inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone inexact Newton scheme, we present the convergence theorems. Finally, we show how we can apply these strategies to the inexact Newton interior-point method and we present some numerical examples.
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