On 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, considered in this work, allows one to solve also nonlinear equations with geometric constraints and systems of inequalities in a unified manner. The emphasis is given to systems of linear inequalities. The study of the well-posedness of the algorithm and of its convergence is fulfilled in the framework of modern variational analysis.