Recent applications of Quasi-Newton Methods for solving nonlinear systems of equations

The quasi-Newton methods have been very used in the solution of nonlinear systems that appear in the most applied areas, such as Physics, Engineering, Chemistry and Industry. Many times some methods of this family are developed and analyzed for a solution of particular problems, for example as in the case of nonlinear complementarity problems.In this work we study several recent applications of quasi-Newton methods for solving nonlinear systems of equations. It is a fundamental part of this work, a careful bibliographical research via Libraries and also via Internet, for a selection of the applications. We hope we have made an understandable abstract of the applications chosen and of the quasi-Newton methods used, in each of them.With this work we believe that we elaborated a diagnosis of the status of the quasi-Newton methods in the solution of real life problems, answering thus, questions like: (i) are there problems, in the applied research, for which the quasi-Newton methods are the best option? (ii) which are they? (iii) why?