Parallel Algorithms for Solving the Convex Minimum Cost Flow Problem

In this paper we deal with the solution of the separable convex cost network flow problem. In particular, we propose a parallel asynchronous version of the relaxation method and we prove theoretically its correctness. We present two implementations of the parallel method for a shared memory multiprocessor system, and we empirically analyze their numerical performance on different test problems. The preliminary numerical results show a good reduction of the execution time of the parallel algorithm with the respect to the sequential counterpart.