On convexity tags

Question

The tags on convexity are convex-geometry ($\times$560), convex-analysis ($\times$ 266), convexity ($\times$ 420). Here the number is the current (2019/02/23) number of uses and I ignore some more specific tags whose meaning is quite well-identified such as convex-polytopes or convex-optimization.

The tag convex-geometry currently (2019/02/23) has the usage guidance: A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ... Also, convexity and convex-analysis have no usage guidance at this date.

Vaguely:

How could this be improved?

Adding tag guidance would require to have a more precise idea how to distribute the roles of these tags. But I see no coherent way to do so.

I see two essential meanings for "convexity": convexity of functions (closer to convex analysis) and convexity of bodies (closer to convex geometry, which also encompasses convexity in metric spaces). The distinction is clear in a number of cases, but this is also well-intertwined since convex functions are usually defined on convex subsets, while convex sets can usually be defined as sub-level sets of convex functions.

At this moment, a quick look at the actual use of convexity seems to be a slight majority of questions on convex functions, an a large minority of convex geometry questions, and it's regularly used in combination with one of the other two tags (40%? I made no serious count).

At this point I see among the various options:

1. Keep these 3 tags. I guess this considers that convexity is the union of convex-analysis and convex-geometry. Improve usage guidance accordingly (how?) to avoid a too random use. Clarify when should convexity be used: when both others are applicable? when at least one is applicable?
2. Deprecate convexity and use the two others (one or both).
3. Make both convex-analysis and convex-geometry synonyms of convexity, considering that the difference is not significant enough and that a broader tag would benefit.

Others options are welcome. The only thing I'm convinced is that statu quo is not a good option.

---

Edit: (to take into account Martin Sleziak's comment)

Here is a 2017/09/27 comment by François G. Dorais♦ about this issue:

"convexity is perplexing since it's almost a meta-tag. My preference would be to have these questions remapped to convex-analysis, convex-geometry, and similar. However, this seems very implausible at the moment."

The closest option above is the technically easy (2), solving the issue for future questions. If one wants to solve the issue for past questions, if one wants to completely delete convexity, one could imagine (if technically doable): remove convexity from every question with at least one of the other 2 tags; for those tagged convexity and none of the other 2, remove convexity and add the other two (this will block for a few remaining ones for which there are already 5 tags but one can imagine these few can be dealt manually). But this can sound arbitrary, so just deprecating sounds enough, while users can then progressively manually delete past occurrences of deprecated convexity.

Answer 1

To go forth, here's one single suggestion, namely an expanded version of (2) in my question, namely do the following three things:

a) convex-geometry: its current tag guidance (which can be amended anyway, as any tag) is: "A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...". Add "Can be used in combination with related tags such as convex-polytopes, convex-analysis, etc".

b) Add a tag guidance to convex-analysis. Here's a suggestion (which can be improved now or afterwards): "Convex functions, analysis on convex sets. Can be used in combination with related tags such as fa.functional-analysis, convex-geometry, convex-optimization, etc."

c) Deprecate convexity. Namely, change its (currently empty) tag guidance to "Deprecated: do not use this tag. Instead, use convex-geometry, convex-analysis, or related tags".

All this is easy to do, so if we agree let's go, and we can discuss afterwards about past posts tagged convexity.