Algorithms and software for multilevel nonlinear optimization

This research concerns the algorithmic study of multilevel nonlinear optimization problems. We have developped during our thesis new methods to solve this type of problems and we analyze their convergence and numerical results. We have also implemented a soft- ware for which a complete description is given in this manuscript. A library of test problems has also been constructed on which we have tested our software. The numerical results ob- tained show that our method is clearly the best for this class of problems. The software also allowed the solution of a progressive lens industrial application that had never been solved by existing methods.