There is a slight strangeness in the current tagging system related to tags for maxima and minima. Martin and I discussed this at some point, we did not have quite the same view, and it concerns quite a few questions, so here is the situation to be resolved.

The tags , , , are all synonyms of .

The tag is not yet but has a synonym proposed, and has more than 1000 questions.

The tag exists also and has and as synonyms.

The question is mostly should be also put into the group (that is should the synonym be approved and a merge performed), or instead should at least and maybe be taken out of the group and combined with (and possibly also the but that's a side question).

The current situation that persists since a while seems in any cases inconsistent, and should be about the same.

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    I know about the tag management thread, I posted a separate question on purpose, as the tags are quite large. – quid Aug 25 at 0:53
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    For context, here's the discussion (rather uncontroversial) from when max-min was originally made a synonym of optimization: math.meta.stackexchange.com/questions/9128/… – Eric Wofsey Aug 25 at 2:27
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    Max-min sounds like a tag more appropriate for questions related to a theorem by von Neumann, or its relatives. That makes it related to, but distinct from, maxima-minima. Admittedly, that doesn’t seem to be how the tag has been used. – Theoretical Economist Aug 25 at 14:14
  • @TheoreticalEconomist something related came up very recently see this comment in chat That tag was then removed on the grounds that it was too vague with a referenc I am not sure I agree with that removal, but I did not think much about it. But, yes, maybe min-max as a tag is not that useful (as explained in my answer I could well imagine to just remove it, too). – quid Aug 25 at 14:40

The tag should not be a synonym of , neither should be the tag .

Given the historical tag description of I'd agree that it was reasonable to propose it then, but I still think it is not a good idea.

The reason for my view is that those notions, maximum and minimum, also arise sometimes in contexts that have nothing to do with optimization, and often arises in contexts where the link to optimization is tangential.

For the former I think of usage with respect to order relations in general. Abstractly, one could also make a case that a tag for maximum and minimum should be a synonym of . (It should not be, either, but it would be just as valid as optimization, in my opinion.)

For the latter I mean all the calculus questions that ask for local maxima and minima of some function maybe together with poles and asymptotes. That's not really about optimization. I think having all those under somewhat pollutes the tag, which should be dedicated to questions that are actually about optimization.

Or, questions about whether some set of real number has a maximum, that's not optimization. (Right, one could construe it as a question about extrema of the identity function, but that's contrived.)

Thus, my proposal is to keep the tag separate and to make a synonym of that tag (or to remove it entirely). I'd do the same with but that's a bit less important.

Generally, I think we should avoid all synonyms where there is a risk that questions get a tag that is just wrong for the question. Ambiguous tags should either be accepted or they should be avoided, but they should not be synonyms of one of several use-cases, even if that is the most common one.

  • max-min is used in game theory/calculus of variations, and it is not about finding maxima or minima (it's more about finding saddle points). So making that a synonym seems incorrect. – user99914 Aug 25 at 15:52
  • and there are post tagged with both optimization and game theory, which may be the results of the existing synonym. For example, this should not be tagged optimization. – user99914 Aug 25 at 15:54
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    As an aside, recently someone created minimax-theory and I removed it. Not that I completely disagree with its existence, but I think a discussion is needed since the term min-max means so many things in mathematics. – user99914 Aug 25 at 15:59
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    @JohnMa indeed, I referenced that in a comment on main. Thanks for the input on max-min. Maybe it is not good as a tag at all then, or should be max-and-min to avoid the confusion, or max and min as separate tags. – quid Aug 25 at 16:09

Some of the difficulty of treating certain of these closely related tags is due to an awkward overlap between the topics of "optimization" and "approximation theory".

These are connected subjects, but they have significantly different foci and techniques. Optimization usually requires a single scalar valued objective function, while approximations are often useful in sub-optimal forms, e.g. in density arguments.

I'm happy leaving many of these tags as independent labels, not trying to identify them with the somewhat high level notion of . I'm particularly fond of rational approximations, where alternating location of maxima and minima play a central role in the Reméz algorithm.

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