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Next Generation Networks (NGN) are envisaged to see a vast and inevitable convergence of diverse multimedia and mobile services with versatile bandwidth utilities. As such, a design challenge for NGN is to allow efficient rate allocation without compromising Quality of Service (QoS) provisioning to any service and thereby enable a global welfare gain. However, the traditional rate allocation schemes assume elasticity of application services and strict-concavity of utility functions. Such assumptions provide design simplicity, but in practice, limit the applicability of resulting protocols, in that severe QoS problems are encountered when bandwidth is shared by inelastic services with non-concave utility functions. As such, the current strict priority based schemes cannot maximize the overall network utility for NGN, and hence bring a significant global welfare loss. This paper presents an adaptive rate control algorithm to distributively allocate transmission rates to multiclass services. The proposed algorithm is based on the Lagrangian Relaxation for a dual formulation by decomposing the rate allocation problem into a master-slave framework. We use a novel surrogate subgradient method to solve the master problem. For the nonconvex subproblems, we compare the performance of a number of global optimization methods, where the objectives are to achieve fast convergence as well as accuracy.