A scaled reduced gradient algorithm for network flow problems with convex separable costs

In this paper we present an algorithm for the convex-cost, separable network flow problem. It makes explicit use of the second-order information and also exploits the special network programming data structures originally developed for the linear case. A key and new feature of the method is the use of a preprocessing procedure that resolves the problem of degeneracy encountered in reduced gradient methods. Some preliminary computational experience with the algorithm on water distribution problems is also presented. Its performance is compared with that of a reduced gradient and a convex simplex code.

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