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The paper discusses a new view on globalization techniques for Newton’s method. In particular, strategies based on “natural level functions” are considered and their properties are investigated. A “restrictive mono-tonicity test” is introduced and theoretically motivated. Numerical results for a highly nonlinear optimal control problem from aerospace engineering and a parameter estimation for a chemical process are presented.

On the Role of Natural Level Functions to Achieve Global Convergence for Damped Newton Methods