# A Strongly Polynomial Algorithm for a Class of Minimum-Cost Flow Problems with Separable Convex Objectives

@article{Vgh2016ASP,
title={A Strongly Polynomial Algorithm for a Class of Minimum-Cost Flow Problems with Separable Convex Objectives},
author={L{\'a}szl{\'o} A. V{\'e}gh},
journal={SIAM J. Comput.},
year={2016},
volume={45},
pages={1729-1761}
}
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E}C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a strongly polynomial algorithm for the case when all $C_{ij}$'s are convex quadratic functions, settling an open problem raised, e.g., by Hochbaum [Math. Oper. Res., 19 (1994), pp. 390--409]. We also give strongly polynomial algorithms for computing market… CONTINUE READING

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