Timeline for Does approximately null gradient imply approximately global minimum for convex functions?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1 at 8:15 | vote | accept | R. W. Prado | ||
| Dec 1 at 7:55 | vote | accept | R. W. Prado | ||
| Dec 1 at 7:59 | |||||
| Dec 1 at 3:33 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Dec 1 at 1:08 | comment | added | R. W. Prado | For a convex set with bounded vanishing set, it is only necessary to see that the function is coercive and that $f(x) \leq \|\nabla f (x)\| \text{dist} (x, \Omega)$, where $\Omega$ is the vanishing set. To see that the function is coercive, just notice that, there is a positive $\delta$ so that $f (x) \geq \delta \|x\|$ for $\|x\|$ big enough . | |
| Nov 30 at 6:15 | comment | added | R. W. Prado | Here is quite late, however, I strongly suspect that it has to do with Theorem 1.10 and Corollary 1.14 of esaim-proc.org/articles/proc/pdf/2003/01/aze.pdf. These types of error bound rarely are not satisfied far from the solution set, since the gradient of the objective function does not vanish (LICQ is satisfied). | |
| Nov 30 at 5:04 | comment | added | R. W. Prado | This question was also asked on the website: math.stackexchange.com/questions/5005166/… | |
| Nov 30 at 5:03 | history | asked | R. W. Prado | CC BY-SA 4.0 |