## Solving Nonlinear Multicommodity Flow Problems By The Analytic Center Cutting Plane Method (1995)

Citations: | 29 - 14 self |

### BibTeX

@MISC{Goffin95solvingnonlinear,

author = {J.-L. Goffin and J. Gondzio and R. Sarkissian and J.-P. Vial},

title = {Solving Nonlinear Multicommodity Flow Problems By The Analytic Center Cutting Plane Method},

year = {1995}

}

### OpenURL

### Abstract

The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems. Each subproblem consists of finding a minimum cost flow between an origin and a destination node in an uncapacited network. It is thus formulated as a shortest path problem and solved with the Dijkstra's d-heap algorithm. An implementation is described that that takes full advantage of the supersparsity of the network in the linear algebra operations. Computational results show the efficiency of this approach on well-known nondifferentiable problems and also large scale randomly generated problems (up to 1000 arcs and 5000 commodities). This research has been supported by the Fonds National de la Recherche Scientifique Suisse, grant #12 \Gamma 34002:92, NSERC-Canada and ...