Timeline for Example of convex functions fulfilling a (strange) lower bound
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 16, 2019 at 16:59 | vote | accept | Y.B. | ||
| Jan 15, 2019 at 14:43 | answer | added | Dirk | timeline score: 3 | |
| Jan 15, 2019 at 14:31 | comment | added | Y.B. | @YoavKallus That is also good try, thanks. The point in choosing small $|\gamma|$ is to ensure non negativity, right? This seems an interesting example disjoint from the class indicated by iosif Pinelis. Thanks you. | |
| Jan 15, 2019 at 14:07 | comment | added | Yoav Kallus | The form of (3) suggests $a|x| - \langle \gamma, x\rangle$ as a possibility. Doesn't that work (for small enough $|\gamma|$)? | |
| Jan 15, 2019 at 14:05 | answer | added | Iosif Pinelis | timeline score: 4 | |
| Jan 15, 2019 at 13:20 | review | Close votes | |||
| Jan 17, 2019 at 13:08 | |||||
| Jan 15, 2019 at 13:18 | comment | added | Y.B. | @AlexandreEremenko I see your point and thanks for the comment, yet I am looking for a completely "different" example. I have not written it in the OP (to avoid being too long and verbose) but this function $f$ plays the role of integrand of a min problem in CoV, i.e. $\min \int_\Omega f(Du) dx$ among suitable competitors $u$. I am not interested into the case $f(\cdot) = \vert \cdot \vert$ (which is well-known) and, as you can now see, multiplicative constants do not play any role. | |
| Jan 15, 2019 at 13:02 | history | edited | Y.B. | CC BY-SA 4.0 |
added 48 characters in body
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| Jan 15, 2019 at 13:00 | comment | added | Alexandre Eremenko | Then take $k|x|$, $k>0$. | |
| Jan 15, 2019 at 12:16 | history | edited | Y.B. | CC BY-SA 4.0 |
added 149 characters in body
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| Jan 15, 2019 at 12:15 | comment | added | Y.B. | @πr8 Sure, I forgot to mention that I am looking for another function than the norm :-) You are perfectly right, thanks! | |
| Jan 15, 2019 at 11:58 | comment | added | πr8 | Does $f(x) = |x|$ not work? | |
| Jan 15, 2019 at 11:41 | history | asked | Y.B. | CC BY-SA 4.0 |