Timeline for Differentiability of distance to a closed convex set [closed]
Current License: CC BY-SA 4.0
19 events
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| Dec 12, 2022 at 1:36 | history | edited | YCor | CC BY-SA 4.0 |
added nonempty for function to be defined; removed capitals
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| May 18, 2019 at 10:01 | comment | added | Paul Taylor | See also my <a href="mathoverflow.net/questions/331782/… question</a> with application to constructive analysis | |
| May 17, 2019 at 19:50 | review | Reopen votes | |||
| May 17, 2019 at 22:40 | |||||
| May 17, 2019 at 14:31 | comment | added | xel | Usually the better object to study is $d(\cdot,A)^2$ (note the square), as this function has the desired properties, if $|| \cdot ||$ stems from an inner product. | |
| Aug 17, 2016 at 17:06 | history | closed |
Anton Petrunin Myshkin user21574 Alexey Ustinov Stefan Kohl♦ |
Not suitable for this site | |
| Aug 17, 2016 at 12:47 | answer | added | Aryeh Kontorovich | timeline score: 8 | |
| Aug 17, 2016 at 10:40 | review | Close votes | |||
| Aug 17, 2016 at 17:06 | |||||
| Aug 17, 2016 at 9:13 | comment | added | Włodzimierz Holsztyński | @FedorPetrov and AmirSagiv and everybody, sorry. I missed word convex, of course. | |
| Aug 17, 2016 at 9:04 | comment | added | Fedor Petrov | @WłodzimierzHolsztyński This set $A$ is not convex. | |
| Aug 17, 2016 at 8:34 | comment | added | Włodzimierz Holsztyński | Consider $\ A := \{x\in R^d : ||x|| \ge 1\}.\ $ The $\ d(x,A)\ $ is not differentiable at $0\in R^d,\ $ for every $d=1\ 2\ldots\ $ BTW, it'd be more interesting to consider the square of the distance. | |
| S Aug 17, 2016 at 7:03 | history | suggested | Amir Sagiv |
removed linear algebra and functional analysis tags, which were irrelevant, and added the metric geometry and metric spaces
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| Aug 17, 2016 at 6:43 | comment | added | Aryeh Kontorovich | In general, you'll only have differentiability issues at the boundary of $A$. | |
| Aug 17, 2016 at 6:40 | comment | added | Aryeh Kontorovich | Later in that exercise (d.iv), the gradient is computed for $x\notin A$. | |
| Aug 17, 2016 at 6:38 | comment | added | Aryeh Kontorovich | Borwein+Lewis Convex Analysis, Section 3.3 Exercise 12(d.iii) characterizes the subdifferential of this function. | |
| Aug 17, 2016 at 6:33 | comment | added | Fedor Petrov | Take $A=\{0\}$, $d(x,A)=\|x\|$ is not differentiable at 0. | |
| Aug 17, 2016 at 6:20 | review | Suggested edits | |||
| S Aug 17, 2016 at 7:03 | |||||
| Aug 17, 2016 at 6:18 | comment | added | Amir Sagiv | @WłodzimierzHolsztyński , can you refer or give a counter example? | |
| Aug 17, 2016 at 6:07 | comment | added | Włodzimierz Holsztyński | In general, this distance is not differentiable already in $R^2$ at a point $p\in R^2\setminus A$. | |
| Aug 17, 2016 at 5:02 | history | asked | Steve | CC BY-SA 3.0 |