Network utility maximization with path cardinality constraints

In this paper, we study network utility maximization over both routing choice and path rate assignment for any given path cardinality constraint. We provide a novel convex relaxation, which leads to a randomized algorithm with performance guarantees. The new relaxation also enables distributed algorithm design and allows us to obtain performance estimation for nonconvex routing optimization problems that is significantly better than previous work based on the multipath routing relaxation. Convergence and performance of the proposed randomized algorithm are characterized theoretically and further illustrated numerically through examples to demonstrate its superiority over existing work.

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