Talk:Convex set
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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
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
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.
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)
[edit] Category:Topology
I do not think topology has anything to do with convexity....Tosha 12:19, 5 Jul 2004 (UTC)
Convex implies contractible, but after that, I probably agree. Charles Matthews 12:28, 5 Jul 2004 (UTC)
- I only wanted to say that it should not be in Category:Topology (hope you agree) Tosha 11:13, 6 Jul 2004 (UTC)
OK, the topology category isn't really useful. Charles Matthews 14:15, 6 Jul 2004 (UTC)
It may just be me, but shouldn't this page also include a simple picture to illustrate as well? The mathematical properties may not be what everyone is looking for when they come here.
This absolutely should be under Category:Topology too, but it needs to be changed to allow that: add the topological definition of convexity. This is what I came here looking for...if I cant find it here, where should I find it? Rob 00:11, 21 November 2005 (UTC)
[edit] Star Convexity
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)
EDIT: Added it anyway :-P cBuckley 13:40, 10 February 2006 (UTC)
[edit] Convex polygon
Convex polygon would fit in here greatly. --Abdull 14:23, 17 May 2006 (UTC)
