Separable convexification and DCA techniques for capacity and flow assignment problems

We study a continuous version of the capacity and flow assignment problem ( CFA) where the design cost is combined with an average delay measure to yie ld a non convex objective function coupled with multicommodity flow constra ints. A separable convexification of each arc cost function is proposed to obtain approximate feasible solutions within easily computable gaps from op timality. On the other hand, DC (difference of convex functions) programmin g can be used to compute accurate upper bounds and reduce the gap. The tech nique is shown to be effective when topology is assumed fixed and capacity expansion on some arcs is considered.