As deep learning penetrates into wide application domains, it is essential to evaluate the robustness of deep neural networks (DNNs) under adversarial attacks, especially for some security-critical applications. To better understand the security properties of DNNs, we propose a general framework for constructing adversarial examples, based on ADMM (Alternating Direction Method of Multipliers). This general framework can be adapted to implement L2 and L0 attacks with minor changes. Our ADMM attacks require less distortion for incorrect classification compared with CW attacks. Our ADMM attack is also able to break defenses such as defensive distillation and adversarial training, and provide strong attack transferability.