A parametric approach for maximum flow problems with an additional reverse convex constraint

This paper considers maximum integral flow problems with an additional reverse convex constraint involving one or two nonlinear variables. Based on a parametric approach, it proposes a polynomial-time algorithm for computing an integral flow globally optimal to the problem with a single nonlinear variable. The paper extends this idea and solves the problem with two nonlinear variables. The algorithm solves a sequence of ordinary minimum cost flow problems by using a conventional method and yields a globally optimal solution in pseudo-polynomial time.