What to do when a referee asks me to do something impossible/unreasonable? What are my best options when a reviewer misunderstands my work and asks for an unreasonable improvement? She was very clear that this was a major issue and that she would only accept the paper under this "improvement".


Should I withdraw the submission?
Should I write to the editor and try to convince him that the reviewer is wrong? (Possibly asking for a new reviewer).
Should I make the revision normally trying to convince editor and referee that what they ask is impossible?
Something else?


I'm inclined to go with the 2nd option.

The field is in the intersection of Mathematics and Computer Science, and the journal is not a top one.

Edit: I've made the revision normally, as suggested here. Thanks to everyone that commented as I wouldn't have done so. In the end, I was happy with the revision.
I believe the key is that you can include the information in your paper about this direction being "impossible", and improve it significantly by doing so.

Rather than rejecting the suggestion outright, add a discussion to your paper of that future direction and some notes on its difficulty (i.e., although we show in this paper that 10+10=20 through novel use of the podal digits, the corollary of 20-10=10 cannot currently be proven empirically due to limitations of the primary technique of positive incremental dactylonomy, and the lack of willing test subjects for the secondary approach).

Although it might seem obvious to you why that improvement is "impossible", your reviewers may read your paper even more carefully than your broader audience. If something was unclear (or at least, non-obvious) to this reviewer, you should expect that at least some non-negligible proportion of your broader readership will come to the same conclusion. I think you improve your paper substantially if you can explain this concisely.

Even better, if you can suggest some approach that is possible but currently difficult to implement or outside the scope of your current paper, your work could be the priority reference for that approach.