Talk:Convex set

message: I think the title of the section "In Euclidean geometry" is misleading since the content of the section is much more generel than this...  —Preceding unsigned comment added by 130.226.45.151 (talk) 17:48, 16 November 2009 (UTC)

message: I took out the phrase "corresponding to regular polyhedra" because it didn't fit in the sentence and because it didn't convey important information. I guess one could rephrase the sentence to include the information that Platonic solids are regular polyhedra, but I didn't bother. --AxelBoldt
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The following was added:
:One application of convex hulls is found in efficiency frontier analysis. Efficiency is assumed to be a monotonic function of each of finitely many of real variables. Each one of finitely many data points is in exactly one hull, and is considered more efficient than all data points in hulls contained within its own hull. A particle whose velocity vector has a value of a for all coordinates representing maximized variables, and a value less than a for all minimized variables, will pass through the hulls in increasing order of efficiency.
I do not understand this. Are we talking about efficiency frontiers in the sense of http://library.wolfram.com/webMathematica/MSP/Explore/Business/Frontier ? What does "maximized variable" refer to? AxelBoldt, Tuesday, June 11, 2002
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In the most commonly discussed type of efficient frontier, one wishes to maximize average return and minimize variance of return.  For this purpose the efficient frontier is the "northwest" hull of a plot of portfolios with mean return as the y coordinate and standard deviation of return as the x coordinate.  The y-intercept, not surprisingly, is called the "risk-free rate".
I suppose the southeast hull could be called an "inefficient frontier".  The same method of analysis is used in other optimization problems, using other numbers of variables.  Some optimizations might seek to maximize all variables, or minimize some and maximize others.  In any case, the efficient set is some convex portion of the outer hull of the points.  This, of course, is assuming a large number of proposed solutions have been designed and had their specifications calculated and tabulated.
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With regard to the discussion of convex sets, to see if I got this right, would it be correct to call a set of number whose coordinates in the complex plane form a convex polygon a convex set (or complex convex set)? Fredrik 15:30, 28 May 2004 (UTC)
thread_title: ?

message: I do not think topology has anything to do with convexity....Tosha 12:19, 5 Jul 2004 (UTC)
replies: text: I only wanted to say that it should not be in Category:Topology (hope you agree) Tosha 11:13, 6 Jul 2004 (UTC)
thread_title: Category:Topology

message: Was thinking of adding the notion of star-convex sets. What does anyone think about including it here? It's not really a big enough topic to have its own page. cBuckley 12:30, 10 February 2006 (UTC)
thread_title:  Star Convexity 

message: Convex polygon would fit in here greatly. --Abdull 14:23, 17 May 2006 (UTC)
thread_title:  Convex polygon 

message: I would say that we should mention quasi convex in the article too.
& strongly, strictly quasi convex. & semi convex. Jackzhp (talk) 17:08, 13 September 2008 (UTC)
replies: text: As far as I know, quasiconvexity is a concept that generalizes convex functions, not convex sets. The convex function article does mention quasiconvex functions in its see-also section, but I suppose that could be better integrated into the text of the article. —David Eppstein (talk) 21:09, 28 November 2008 (UTC)
thread_title: convex vs. quasi convex

message: It is erroneous to have a picture with the legend/title "non-convex (i.e., concave)". 
A halfspace is a convex set whose complement is convex, for example. 
It might be useful to discuss quasi-convex sets and pseudo-convex sets, from the standpoint of (Rockafellarian) variational analysis, by discussing the epigraphs and lower levelsets of the (convex-analytic) indicator functions (or set-theoretic indicator functions) for such sets, i.e., the functions's quasiconvexity or pseudoconvexity. 
(This suggestion accords with the comments of some previous discussants.) 
However, such definitions are incompatible with the usage of several complex variables. Kiefer.Wolfowitz (talk) 18:39, 24 June 2009 (UTC)
thread_title:  "Concave set" versus a "set with a concavity" versus "a nonconvex set" 

message: Convex curve is logically contained within convex set topic. Also, wiki entry on the former is literally just one statement. IT seems appropriate to merge it with convex set. Mittgaurav (talk) 08:40, 31 December 2011 (UTC)
replies: text: It is not clear from that one statement if the boundary of a convex set in any number of dimensions is called a convex curve, or if what is meant is rather a convex function. I think a reference is needed to sort this out. Isheden (talk) 11:06, 31 December 2011 (UTC)
thread_title:  Merge Convex curve with this page 

message: Perhaps this picture of the german wikipedia is useful in the article:
http://de.wikipedia.org/wiki/Datei:KonkaveFiguren.png
--Flegmon (talk) 11:58, 26 April 2012 (UTC)
replies: text: I think the existing picture that illustrates a non-convex set is better than these examples. It is misleading to indicate the midpoints of the connecting lines, since it is not enough that the midpoint is in the set. Rather, all points on the connecting line have to be in the set. In the present example, all points that lie outside the set or highlighted in red. Isheden (talk) 12:15, 26 April 2012 (UTC)
thread_title:  helpful picture of counterexamples 

message: "Complex convexity" is just a special case of "convex set" where you're operating in C^n - no need to have a whole other article. Enterprisey (talk!) 04:44, 8 September 2018 (UTC)
replies: text: I think C^n is different enough from R^n, and (real) convexity is basic enough, that this would be overly confusing and WP:TECHNICAL as an addition to the convex set article. And I don't see why we should privilege this notion over the five other generalizations of convexity already listed (in summary style) in the "Generalizations and extensions for convexity" section of the convex set article; what makes it deserve full elaboration here, rather than another summary-style entry, besides the fact that the existing complex convexity article is so stubby and incomplete? —David Eppstein (talk) 05:51, 8 September 2018 (UTC)
replies: text: , I'm proposing that Complex convexity be merged into this article. I strongly agree with you that it's weird to have special treatment for this topic - I would rather complex convexity be listed in that section, with Complex convexity being a redirect to it. Enterprisey (talk!) 06:35, 8 September 2018 (UTC)
replies: text: To be treated equally, it should be handled in summary style, with a pointer here to a separate and more complete article at the existing title. Anything else is special treatment. —David Eppstein (talk) 06:37, 8 September 2018 (UTC)
replies: text: I see what you're saying. I'm not sure that the sources are there to support an article rather than a redirect, but I don't feel particularly strongly about this. I've put a link in the "See also" section for the time being. Enterprisey (talk!) 06:44, 8 September 2018 (UTC)
replies: text:  The reply may be too late, but I think it's related to Pseudoconvexity. In that article, it was linked to plurisubharmonic functions. --SilverMatsu (talk) 05:49, 11 January 2022 (UTC)
replies: text: I don't have the math knowledge to know how that topic relates to this one, so feel free to do whatever. Enterprisey (talk!) 02:09, 16 January 2022 (UTC)
thread_title:  Proposed merge with [[Complex convexity]] 

message: This is gibberish. For starters, subset is singular, so the verb should be "intersects" - but then we are left with "intersects into a line segment" which is not any kind of maths jargon I have ever heard. 2A01:CB0C:CD:D800:C8A2:EE7F:D271:DFC6 (talk) 08:04, 4 June 2020 (UTC)
thread_title:  is a subset that intersect every line into a single line segment (possibly empty). 

message: "The Minkowski sum of two compact convex sets is compact." -- compact sets are not introduced in this article. Cuppoo (talk) 02:42, 13 December 2023 (UTC)
thread_title:  "Compact" set