An ε-Relaxation Method for Separable Convex Cost Network Flow Problems

We propose a new method for the solution of the single commodity, separable convex cost network flow problem. The method generalizes the $\epsilon$-relaxation method developed for linear cost problems and reduces to that method when applied to linear cost problems. We show that the method terminates with a near optimal solution, and we provide an associated complexity analysis. We also present computational results showing that the method is much faster than earlier relaxation methods, particularly for ill-conditioned problems.

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