Timeline for Boundedness of maximisers of parametric strictly concave functions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 5, 2023 at 14:51 | vote | accept | Fawen90 | ||
| Nov 3, 2023 at 5:05 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Nov 2, 2023 at 21:08 | comment | added | Fawen90 | @IosifPinelis Right. That's why I can not see the explicit dependency of the maximiser on $\lambda$. I'm still seeking for more detailed proofs and will let you know | |
| Nov 1, 2023 at 20:21 | comment | added | Iosif Pinelis | The proof of Proposition 1.9 is based on Proposition 1.7, which is left without proof. So, again, can you provide a reference/link to a proof that a maximizer exists? | |
| Oct 31, 2023 at 15:18 | comment | added | Fawen90 | @IosifPinelis This is the entropic optimal transport, and can be found in the lecture notes lucanenna.github.io/teaching/optimaltransport/lecture2.pdf (Proposition 1.8 and 1.9) Of course, the maximiser $(x,y)$ is unique if we require $x_1=0$ | |
| Oct 31, 2023 at 13:42 | comment | added | Iosif Pinelis | Can you provide a reference/link to a proof that "for every $\lambda\in [0,1]$, $\mbox{argmax}_{\mathbb R^m\times \mathbb R^n}L(\lambda, \cdot,\cdot)$ exists"? Also, clearly, you should rather be asking about compactness "up to the translation" (and define it). | |
| Oct 31, 2023 at 8:27 | history | asked | Fawen90 | CC BY-SA 4.0 |