This paper presents a new duality approach to optimize the resource assignment and bandwidth allocation in networks, which is based on the generalized particle model (GPM). By the GPM, the network’s optimization problem is transformed into the kinematics and dynamics of numerous particles in two reciprocal dual force-fields. Like the Kelly’s duality model and Low’s duality model related to Lagrangian multipliers methods (LMM), the GPM-based duality model also contains two distributed algorithms for resource supplies and resource demands, respectively, and can be carried out in parallel. Both the LMM-based and GPM-based duality models may not only embody the market mechanism between the supplies and demands very well, but also may describe the influence of congestion degree of networks on the resource allocation. But the GPM-based duality model is different from other duality models in terms of the basic principle, mathematical formalization, and properties. Features of the GPM-based duality model and the corresponding duality algorithm include a powerful processing ability in a complex environment that involves the priority, personality, autonomy, and interaction of different entities in networks. Furthermore, the GPM-based duality model can realize the optimization of multiple objectives, including the aggregate utility, the personal utility, the minimal personal utility, the resource utilization, and the users’ satisfactory degree. The proposed approach also has the advantages in terms of the higher parallelism, lower computation complexity, and the ease for hardware implementation. The properties of the GPM-based duality model, including the correctness, convergency and stability, are discussed in detail. The numerous simulations on the network bandwidth allocation have shown the effectiveness and suitability of the proposed approach.