Complexity of the Newton method for set-valued maps

The Newton method is one of the most powerful tools used to solve systems of nonlinear equations. Its set-valued generalization allows one to solve also nonlinear equations with geometric constraints and systems of nonlinear equations and inequalities in a unified manner. In this work some complexity issues concerning the method are studied. The results are illustrated by examples.the Portuguese Foundation for Science and Technologies (FCT), the Portuguese Operational Programme for Competitiveness Factors (COMPETE), the Portuguese National Strategic Reference Framework (QREN), and the European Regional Development Fund (FEDER