Timeline for Inf of Jensen's inequality
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 25, 2018 at 5:33 | vote | accept | yoshi | ||
| Feb 25, 2018 at 5:25 | answer | added | Nate Eldredge | timeline score: 7 | |
| Feb 25, 2018 at 5:18 | comment | added | yoshi | aha! ya got it, add it as answer so I can accept! thx | |
| Feb 25, 2018 at 5:15 | comment | added | Nate Eldredge | Jensen's inequality $\int c(f)\,d\mu \ge c(\int f\,d\mu)$ is always equality when $f$ is constant, so you would want $dz/dt$ to be constant to saturate. That means $z(t)$ has to be linear, and since you know the endpoints, you're done. Also useful to know is that when $c$ is strictly convex, a constant (almost everywhere) is the only way to saturate. | |
| Feb 25, 2018 at 5:09 | history | edited | yoshi | CC BY-SA 3.0 |
added 221 characters in body
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| Feb 25, 2018 at 5:07 | comment | added | yoshi | ya, plugging it in works. maybe i should have asked -- how can I see that's the solution. I tried using a direct method of calculus of variations and was getting mixed up. | |
| Feb 25, 2018 at 3:48 | comment | added | Anthony Quas | Just consider the straight line path with constant speed: $z(t)=(1-t)x+ty$. | |
| Feb 25, 2018 at 3:09 | history | asked | yoshi | CC BY-SA 3.0 |