SIAM Journal on Numerical Analysis
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.
Pawlowski, R. P., Simonis, J. P., Walker, H. F., & Shadid, J. N. (2008). Inexact Newton Dogleg Methods. SIAM Journal on Numerical Analysis, 46(4), 2112-2132. http://dx.doi.org/10.1137/050632166
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© 2008, SIAM Publications.