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I received a major revision decision from IEEE Transactions and one of the reviewer comments is as follows:

"With the defined optimization problem and optimization method, wouldn't this yield a closed-form solution to the problem? How is this described?"

I do not understand the question which prevents me to write the appropriate response. Can anyone please explain what does the reviewer want out of this comment and how should I respond to it.

Thanks

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    I don't think this can be answered without having the context of the paper; and even then, it probably needs someone knowledgeable in this specific research area. I don't think this site is the right place to get an answer. I'd suggest asking a colleague (and showing them your manuscript), or else responding to the editor to see if they can ask the reviewer to clarify. – Nate Eldredge Jun 20 at 19:46
  • With a little bit more context on the problem that your paper attempts to solve (currently, one would have to guess too much), this question will be on-topic at Computational Science SE. If you decide to proceed, please, add some details and (after adding details) either ask a moderator for migration or delete this question and ask a new one. – Anton Menshov Jun 20 at 20:01
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    I will hazard a guess - as you surely know, a closed-form solution implies a standard formula, i.e. does not depend on numerical approximations or simulations to yield a result. I guess you use such a method but the referee knows enough of the area to wonder whether you really need e.g. a simulation or can come up with a closed-form solution (as might be the case in similar problems) if you look at the problem more carefully. If yes, how does that look like? If no, what is the closest you can get? If not clear, why do you need approximation A and not B? – user117109 Jun 20 at 20:38
  • Reviewer is probably asking you to form the dual function, sets its derivative to zero, and get the closed-form expression to calculate the optimal solution. – Prof. Santa Claus Jun 20 at 23:17
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A closed-form solution solves a problem in terms of a finite number of functions/operations from a "standard" set. If your method solves the optimization problem in a defined number of steps, it could potentially be described as closed form. In which case, you could describe this by writing the algorithm as pseudocode and/or providing equations establishing that your solution is closed form. It's likely that adding or substantially revising content is expected as you've been asked to make major revisions.

If your solution is closed-form, I think the main consideration is if whether that adds to the focus of your paper. If it isn't relevant, it'd probably be best to include pseudocode/equations in an appendix. You could also reply that "it's a closed form solution for insert reasons; however, we don't think that extended discussion will add to the focus of the paper (insert paper focus)".

If your solution is not closed-form, reply that "the solution is not closed form as insert reasons".

If you're still unsure and have asked your colleagues, I would reply that "we're unsure specifically what you're asking". Ideally, this would be followed by comments addressing a couple of possible interpretations.

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    I think the reviewer comment is saying that their should be closed form solution to the optimization problem but that the author has proposed an unnecessary iterative approach to solving the optimization problem. – Brian Borchers Jun 20 at 23:14
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    This is the “official” definition of closed form, but I tend to unofficially think of a closed form solution as something that can be calculated directly from the inputs without needing an iterative solver. – Eric Jun 20 at 23:15

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