Optimization of telecommunications networks with security.

Summary The first part of this thesis deals with a robustness study of corrective predictor interior point algorithms, as well as a decomposition approach of this method for solving multiflot problems. In the second part, we focus on the global security problem whose objective is to determine a multiflot (which transports any request from its origin node to its destination node respecting Kirchhoff's law) and the least cost investment in nominal and reserve capacity that ensures nominal routing and guarantees its survival by global rerouting. In our model, the routings and capacities are fractionable. PSG is then formulated as a large linear problem with several levels of coupling. Its particular structure calls for the use of decomposition algorithms. We propose four methods using the column generation technique. The first two are based on proximal techniques. Their main task is to solve independent quadratic subproblems. The third algorithm is inspired by the interior point approach described in the first part. Finally, we integrate a path elimination procedure into an adaptation of an interior point solver. We report numerical results obtained by testing these algorithms on real data provided by the CNET.