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A Newton method for convex separable network flow problems
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DOI：10.1002/net.3230130310.png)
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AbstractPrevious feasible direction algorithms for convex, separable network flow problems that have appeared in the literature have all been linearly convergent. In this paper we propose an approximate implementation of the quadratically convergent Newton algorithm. The key to this implementation is a conjugate direction method that determines second‐order dual multiplier estimates at each iteration. This method exploits the network structure in a way that allows certain crucial matrix‐vector products to be computed in a simple pass through the arcs. Since this novel approach requires no matrix storage to compute these products, the algorithm can be used for large‐scale problems. Some computational experience with this new algorithm is reported.
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