This paper proposes a novel radiometric compensation technique for cooperative projection system based-on distributed optimization. To achieve high scalability and robustness, we assume cooperative projection environments such that 1. each projector does not have information about other projectors as well as target images, 2. the camera does not have information about the projectors either, while having the target images, and 3. only a broadcast communication from the camera to the projectors is allowed to suppress the data transfer bandwidth. To this end, we first investigate a distributed optimization based feedback mechanism that is suitable for the required decentralized information processing environment. Next, we show that this mechanism works well for still image projection, however not necessary for moving images due to the lack of dynamic responsiveness. To overcome this issue, we propose to implement an additional feedforward mechanism. Such a 2 Degree Of Freedom (2-DOF) control structure is well-known in control engineering community as a typical method to enhance not only disturbance rejection but also reference tracking capability, simultaneously. We theoretically guarantee and experimentally demonstrate that this 2-DOF structure yields the moving image projection accuracy that is overwhelming the best achievable performance only by the distributed optimization mechanisms.