Interior point methods for the optimization of large systems.

Summary New interior point methods are playing an increasingly important role in the optimization of large systems. In this thesis we study in a first part, from a theoretical and numerical point of view, an extension of an interior point algorithm for convex and non convex quadratic programming. This extension uses the idea of the confidence region which can be made explicit through an affine transformation. Under certain assumptions we prove results on the global convergence and on the convergence speed of the algorithm. We also give a practical version of this algorithm, based on a generalization of Lanczos' method for solving indefinite linear systems. This one gives very encouraging results in practice. In the second part, we study from a theoretical point of view an extension of another interior point algorithm for nonlinear optimization with linear constraints. This extension uses the idea of reducing a potential function after an affine transformation of the admissible set. Results on the global convergence and on the complexity of the algorithm are given.