Relaxation Methods for Monotropic Programs

We propose a finitely convergent dual descent method for the problem of minimizing a convex, possibly nondifferentiable, separable cost subject to linear constraints. The method has properties reminiscent of the Gauss-Seidel method in numerical analysis. As special cases we obtain the methods in [1] for network flow programs and the methods in [14] for linear programs. *Work supported by the National Science Foundation under grant NSF-ECS-8519058 and by the Army Research Office under grant DAAL03-86-K-0171. The first author is also supported by Canadian NSERC under Grant U0505. tThe authors are with the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139.