Timeline for What is the closed cone generated by constant and coordinate functions and closed under taking $f\mapsto\max(f,0)$?
Current License: CC BY-SA 4.0
11 events
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| Sep 12, 2022 at 2:04 | history | edited | alesia | CC BY-SA 4.0 |
added 26 characters in body
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| Sep 12, 2022 at 1:12 | comment | added | David E Speyer | Okay, I get it now. Interesting question. | |
| Sep 11, 2022 at 19:26 | comment | added | alesia | @Ycor yes that's correct. Starting from two dimensions things seem to get more complicated | |
| Sep 11, 2022 at 18:33 | comment | added | YCor | For $n=1$, is it correct that we obtain exactly all convex non-decreasing functions? | |
| Sep 11, 2022 at 18:14 | comment | added | alesia | @YCor let's say pointwise convergence | |
| Sep 11, 2022 at 18:06 | history | edited | YCor | CC BY-SA 4.0 |
made title more specific, added tag
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| Sep 11, 2022 at 18:04 | comment | added | YCor | You're assuming that the cone is closed with respect to which topology? | |
| Sep 11, 2022 at 17:24 | comment | added | alesia | Also if you add two different functions of the form you described, you might get a function that is not of this form | |
| Sep 11, 2022 at 17:22 | comment | added | alesia | The cone only contains coordinate functions, not their opposite (if you include opposite coordinate functions the cone includes all convex functions) | |
| Sep 11, 2022 at 17:19 | comment | added | David E Speyer | It seems to me that every function in your cone is of the form $f(x_1, x_2, \ldots, x_n) = \max(a_1 x_1, a_2 x_2, \ldots, a_n x_n, -b_1 x_1, -b_2 x_2, \ldots, -b_n x_n, c)$ for some nonnegative constants $a_i$, $b_i$ and $c$. Can you give me an example of a function not of this form? | |
| Sep 11, 2022 at 17:14 | history | asked | alesia | CC BY-SA 4.0 |