I posted a following [question in MSE][1], but I think it should be posted here in MO. Since I don't know how to transfer the post from MSE to MO, I have pasted the question below. Thank you in advance and looking for your comments/suggestions.

My question is two fold:

(1) Is it possible to "solve" (iterative convex/non-convex) optimization problems via learning (e.g., regression / classification) with an objective to "solve" (in some sense) the problem in "one-shot"? 

(2) If the above answer is affirmative, do you have any preferred methods or papers that you can suggest or refer to? 


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ADD: 

Let's consider a following convex optimization whose solution is obtained iteratively via some solver (e.g., CVX). 


\begin{aligned}
& \underset{\mathbf{x} \in \mathbb{R}^n}{\text{minimize}} 
& & \left\| \mathbf{y} - \mathbf{x} \right\|_2^2 %\\
& \text{subject to}
& & \mathbf{A} \mathbf{x}  \leq \mathbf{b} \ ,\\
%&&& X \succeq 0.
\end{aligned}
where the inequality constraint is element-wise. The matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$, vector $\mathbf{b} \geq 0\in \mathbb{R}_{+}^{m}$, and the vector $\mathbf{y} \in \mathbb{R}^{n}$ are given/known. Also, $n > m$, and $n$ can be a very large value.

Question is: can we utilize some "learning" to "predict" the optimal solution (non-iteratively)?

  [1]: https://math.stackexchange.com/questions/2971891/is-it-possible-to-solve-iterative-convex-non-convex-optimization-problems-vi