We present a framework for edge-aware optimization that is an order of magnitude faster than the state of the art while having comparable performance. Our key insight is that the optimization can be formulated by leveraging properties of the domain transform, a method for edge-aware filtering that defines a distance-preserving 1D mapping of the input space. This enables our method to improve performance for a variety of problems including stereo, depth super-resolution, and render from defocus, while keeping the computational complexity linear in the number of pixels. Our method is highly parallelizable and adaptable, and it has demonstrable scalability with respect to image resolution.