Abstract
In this paper, we consider maximum integral flow problems with an additional reverse convex constraint involving one or two nonlinear variables. Based on a parametric approach, we propose a polynomial-time algorithm for computing an integral flow globally optimal to the problem with a single nonlinear variable. We extend this idea and solve 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.
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Kuno, T. A parametric approach for maximum flow problems with an additional reverse convex constraint. Annals of Operations Research 69, 261–276 (1997). https://doi.org/10.1023/A:1018937113330
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DOI: https://doi.org/10.1023/A:1018937113330