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In this letter, we develop a novel computational approach for network bandwidth allocation problems in which the compoundable constraints about the preferable transmission rate fall in the infeasible region. The approach is based on an iterative technique for non-convex optimization over the fixed point set of a certain nonexpansive mapping. The realized allocation maximizes a predefined utility and is closest to the preferable transmission rate with respect to the norm. Numerical examples show that our approach is an efficient way to solve the non-concave utility maximization problem.