Testing Line Search Techniques for Finite Element Discretizations for Unsaturated Flow
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations
SIAM Journal on Scientific Computing
Constrained Dogleg methods for nonlinear systems with simple bounds
Computational Optimization and Applications
| Hi-index | 0.00 |
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.