Timeline for Why does a convex function have to have a convex domain? [closed]
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2017 at 10:29 | comment | added | user32849 | Sorry, this was supposed to go on Math StackExchange. My confusion is like this: if convexity means that I have to be able to draw a line segment between any two points in a graph, and all f(x) within the interval defined by said line have to be below that line, this would hold even if the domain was not convex (e.g. multiple intervals on the reals). | |
| Jan 11, 2017 at 7:05 | review | Reopen votes | |||
| Jan 11, 2017 at 12:57 | |||||
| Jan 11, 2017 at 6:18 | comment | added | asv | In arbitrary domain one can define the notion of locally convex function, i.e. function which is convex in a small convex neighborhood of any point. In case of convex domain this notion of locally convex function is equivalent to the usual notion of convex function. | |
| Jan 10, 2017 at 20:10 | comment | added | Dirk | I would imagine that the definition "I every point there is hyperplane, touching the graph in that point and lying below the graph globally" would work… I don't see any benefit of this, though. | |
| Jan 10, 2017 at 18:55 | history | closed |
Willie Wong R.P. Marco Golla Michael Greinecker Franz Lemmermeyer |
Not suitable for this site | |
| Jan 10, 2017 at 17:08 | review | Close votes | |||
| Jan 10, 2017 at 18:55 | |||||
| Jan 10, 2017 at 16:52 | comment | added | Willie Wong | Alternatively, if one takes the epigraph definition ($f$ is convex is its epigraph is a convex set) then the effective domain of $f$ is necessarily convex. See this and other discussions on page 23 of Rockafeller. | |
| Jan 10, 2017 at 16:41 | comment | added | Michael Greinecker | How would you define a convex function on a nonconvex domain? | |
| Jan 10, 2017 at 16:03 | history | asked | user32849 | CC BY-SA 3.0 |