a quantitative metric for robustness of nonlinear algebraic equation solvers

practitioners in the area of dynamic simulation of technical systems report difficulties at times with steady-state initialization of models developed using general declarative modeling languages. these difficulties are analyzed in detail in this work and a rigorous approach to quantify robustness in the context of nonlinear algebraic equation systems is presented. this tool is then utilized in a study of six state of the art gradient-based iterative solvers on a set of industrial test problems. finally, conclusions are drawn on the observed solver robustness in general, and it is argued whether the reported difficulties with steady-state initialization can be supported using the proposed quantitative metric.