Separable convexification and difference of convex functions techniques for capacity and flow assignment problems

We study a continuous version of the capacity and flow assignment problem where the design cost is combined with an average delay measure to yield a non-convex objective function coupled with multicommodity flow constraints. A separable convexification of each arc cost function is proposed to obtain approximate feasible solutions within easily computable gaps from optimality. On the other hand, difference of convex functions programming can be used to compute accurate upper bounds and reduce the gap. The technique is shown to be effective when topology is assumed fixed and capacity expansion on some arcs is considered.