Inexact Newton Dogleg Methods

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 pr...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2008-01, Vol.46 (4), p.2112-2132
Main Authors: Pawlowski, Roger P., Simonis, Joseph P., Walker, Homer F., Shadid, John N.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Globalization
Iterative methods
Laboratories
Linear algebra
Linear models
Linear systems
Methods
Momentum
Navier Stokes equation
Newton approximation methods
Newtons method
Nonlinear equations
Optimization
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Summary: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.
ISSN:0036-1429
1095-7170
DOI:10.1137/050632166