To address the large model size and intensive computation requirement of deep neural networks (DNNs), weight pruning techniques have been proposed and generally fall into two categories, i.e., static regularization-based pruning and dynamic regularization-based pruning. However, the former method currently suffers either complex workloads or accuracy degradation, while the latter one takes a long time to tune the parameters to achieve the desired pruning rate without accuracy loss. In this paper, we propose a unified DNN weight pruning framework with dynamically updated regularization terms bounded by the designated constraint, which can generate both non-structured sparsity and different kinds of structured sparsity. We also extend our method to an integrated framework for the combination of different DNN compression tasks.