In this paper, we are concerned with the global survivability in telecommunica- tion networks. The objective consists in finding the optimal routing and the least cost investment in base and reserve capacities. The routing and the base capacity insure nominal traffic and the reserve capacity guarantees survivability of the traffic against any arc failure (using a global rerouting strategy). In our model we consider that routings and capacities can be fractional. So the Global Survivability Problem (GSP) can be formulated as a large-scale linear program. Its special structure favours the use of decomposition algorithms. We propose a method using columns generation and proximal decomposition techniques. The main task of this algorithm consists in solving independent quadratic subproblems. We report some numerical results obtained by testing these algorithms with data from the France-Telecom Paris district transmission network.