An ∈-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 ∈-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.