Document Type

Article

Publication Date

4-1-2008

Publication Title

SIAM Journal on Numerical Analysis

Abstract

The dogleg method is a classical trust-region technique for globalizing Newton's method. While it is widely used in optimization, including large-scale optimization via truncated-Newton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexact Newton context and provide a global convergence analysis for it. We then discuss certain issues that may arise with the standard dogleg implementational strategy and propose modified strategies that address them. Newton-Krylov methods have provided important motivation for this work, and we conclude with a report on numerical experiments involving a Newton-GMRES dogleg method applied to benchmark CFD problems.

Volume

46

Issue

4

First Page Number

2112

Last Page Number

2132

DOI

10.1137/050632166

Publisher Statement

© 2008, SIAM Publications.

Included in

Mathematics Commons

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