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This paper concerns the analysis of important algorithmic attributes, namely, the rate of convergence and scalability, and their impact on Network Utility Maximization (NUM). The contribution of the paper is a novel distributed rate control mechanism with strong convergence and scalability properties. The proposed algorithm employs a distinctive distributed framework, where rate control is derived as a Sequential Quadratic Programming (SQP) mechanism incorporated with interior-point and trust-region methods. The NUM problem is solved by a barrier method that penalizes any violation of constraints. Lagrangian is applied to the barrier objective function, where multipliers are estimated using Least-square method to iteratively solve the quadratic approximation of the Lagrangian function at the current point to generate a search direction. The uniqueness of the algorithm is that it allows sources to estimate bandwidth prices and thereby enforces a scalable network core by pushing algorithmic complexity to the edges. The fast convergence of the algorithm, in turn, improves the responsiveness of rate control and enables reduced buffer occupancy. The convergence of the proposed algorithm is proved theoretically and is evaluated via simulations. The results demonstrate reasonable reduction of computation-time in tracking the optimal rates and validate the strong convergence properties of the proposed algorithm.