Video stabilization is usually composed of three stages: feature trajectory extraction, trajectory smoothing, and frame warping. Most previous approaches view them as three separate stages. This paper proposes a method combining the last two stages, namely the trajectory smoothing and frame warping stages, into a single optimization framework. The novelty exists in the way of how we combine them: the trajectory smoothing part plays a major role while the frame warping part plays an auxiliary role. With this kind of design, we can conveniently increase the strength of the trajectory smoothing part by a robust first-order derivative term, which makes it possible to produce very aggressive stabilization effects. On the other hand, we adopt adaptive weighting mechanisms in the frame warping part, to follow the smoothed trajectories as much as possible while regularizing other places as similar as possible. Our method is robust to utilize both foreground and background features, and very short trajectories. The utilization of all these information in turn increases the accuracy of the proposed method. We also provide a simplified implementation of our method, which is less accurate but more efficient. Experiments on various kinds of videos demonstrate the effectiveness of our method.