Step Restriction for a Bounded Newton's Method

摘要

The robustness of Newton's method is improved by modifications which consist of a partial solver for singular equations, use of variable bounds and optional step size bounds through a trust region, step restriction strategies and optional insistence on norm reduction in the NLAEs. The singular equation solver reliably allows escape from singular points. Most problems in a test set could then be solved with hard bounds but no trust region. Of the restriction methods, a partial LP reduction of the linearised residuals was the most effective. Use of a trust region usually helps convergence, but not always. Insisting on norm reduction was a hindrance, except in terminating runs trapped away from a solution. We recommend a methodology for solving NLAE systems. At present this is a procedure to be applied in stages by the user rather than a fully automated algorithm.