I posted a following question in MSE, 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?