Timeline for Lipschitz smooth convex extension
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 17, 2023 at 9:13 | vote | accept | Dmitry Vilensky | ||
| Nov 17, 2023 at 8:48 | answer | added | gerw | timeline score: 2 | |
| Oct 21, 2023 at 18:38 | comment | added | Piotr Hajlasz | As far as I am aware, the answer to the question is not known. | |
| Oct 21, 2023 at 7:29 | comment | added | Dmitry Vilensky | @DustinG.Mixon, I was thinking about this function too, but I was not able to show that its gradient has the same Lipschitz constant. I stuck at the moment of proving non-expansiveness of $y^* =\arg\max_y\{\dotsi\}$ operator, which differs from projection in that it satisfies $\langle \nabla^2 f(y^*)[x-y^*],z-y^*\rangle \leq 0$, and non-expansiveness holds in some specific local norm associated with x,y, which has spectrum proportional to Hessian, so Lipschitz constant scales as well. I don't see how to avoid this :( | |
| Oct 21, 2023 at 1:48 | comment | added | Dustin G. Mixon | I would assume the "right" choice is something like $F(x) := \sup_{y \in S}\big( f(y) + \langle \nabla f(y),x-y \rangle\big)$. | |
| Oct 20, 2023 at 20:32 | history | asked | Dmitry Vilensky | CC BY-SA 4.0 |