I think it's important to note that all of these methods have been largely superseded by deep learning techniques. For example, we can now directly learn algorithms such as gradient descent[1] and classical inverse problems like superresolution are solvable with deep networks [2]. While there still may be a role for tools like CVX, I anticipate all future progress will come from end-to-end differentiable systems.
[1] https://arxiv.org/abs/1606.04474 [2] https://arxiv.org/abs/1501.00092