A novel Lagrangian-relaxation to the minimum cost multicommodity flow problem and its application to OSPF traffic engineering

The minimum cost multicommodity flow problem plays a central role in today´s operations research theory with applications ranging from transportation and logistics to telecommunications network routing. In this paper, we introduce a novel Lagrangian-relaxation technique, which, given an initial feasible solution, can solve the minimum cost multicommodity flow problem as a sequence of single-commodity flow problems. Our methodology is best suited for OSPF traffic engineering, because it can rapidly improve a given path set towards approximate optimality while simultaneously provides the link weights, which implement the paths as shortest paths.