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Trust Region Newton Methods #116
Trust region Newton Methods are a mixture of trust region methods and Newton methods that improves the region of convergence while not sacrificing the "good properties" of Newton near a zero. These methods are important when made quasi-Newton because then you don't need to be diligent about having the right Jacobian and can still get good convergence. This means you can reuse the same Jacobian across different related problems and have an increased convergence range over standard quasi-Newton methods.