Parallel Asynchronous Modified Newton Methods for Network Flows

We consider single commodity strictly convex network flow problems. The dual problem is unconstrained, differentiable and well suited for solution via parallel iterative methods. We propose and prove convergence of parallel asynchronous modified Newton algorithms for solving the dual problem. Parallel asynchronous Newton multisplitting algorithms are also considered, their convergence is also shown. A first set of computational results is presented and analyzed.