Geodesic
The optimal flow in dynamic networks with nonlinear cost functions on edges
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2004), pp. 10-16

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In this paper we study the dynamic version of the nonlinear minimum-cost flow problem on networks. We consider the problem on dynamic networks with nonlinear cost functions on edges that depend on time and flow. Moreover, we assume that the demand function and capacities of edges also depend on time. To solve the problem we propose an algorithm, which is based on reducing the dynamic problem to the classical minimum-cost problem on a time-expanded network. We also study some generalization of the proposed problem. 
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     author = {M. Fonoberova and D. Lozovanu},
     title = {The optimal flow in dynamic networks with nonlinear cost functions on edges},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {10--16},
     publisher = {mathdoc},
     number = {3},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2004_3_a1/}
}
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M. Fonoberova; D. Lozovanu. The optimal flow in dynamic networks with nonlinear cost functions on edges. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2004), pp. 10-16. http://geodesic.mathdoc.fr/item/BASM_2004_3_a1/