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This paper considers a networked system consisting of an operator, which manages the system, and a finite number of subnetworks with all users, and studies the problem of minimizing the sum of the operator's and all users' objective functions over the intersection of the operator's and all users' constraint sets. When users in each subnetwork can communicate with each other, they can implement an incremental subgradient method that uses the transmitted information from their neighbor users. Since the operator can communicate with users in the subnetworks, it can implement a broadcast distributed algorithm that uses all available information in the subnetworks. We present an iterative method combining broadcast and incremental distributed optimization algorithms. Our method has faster convergence and a wider range of application compared with conventional distributed algorithms. We also prove that under certain assumptions our method converges to the solution to the problem in the sense of the strong topology of a Hubert space. Moreover, we numerically compare our method with the conventional distributed algorithms in the case of a data storage system. The numerical results demonstrate the effectiveness and fast convergence of our method. [ABSTRACT FROM AUTHOR]