Timeline for Does this non-negative function, with no stationary points, have only descent directions close to a constraint set?
Current License: CC BY-SA 4.0
22 events
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| Feb 8, 2023 at 23:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 11, 2022 at 23:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 13, 2022 at 23:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 14, 2022 at 21:22 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading while this is on the front page; deleted "Thank you"
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| May 14, 2022 at 10:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 14, 2022 at 10:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 16, 2021 at 10:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 17, 2021 at 9:32 | history | edited | Pietro Majer | CC BY-SA 4.0 |
small typo fixed
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| Aug 17, 2021 at 9:12 | answer | added | Pietro Majer | timeline score: 0 | |
| Aug 8, 2021 at 22:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 10, 2021 at 20:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 11, 2021 at 14:21 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Mar 11, 2021 at 8:54 | history | edited | gmvh | CC BY-SA 4.0 |
Removed inappropriate "descent" tag (it's used in a very different sense on all other questions so tagged)
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| Mar 11, 2021 at 8:02 | comment | added | ARedder | Yes, you are right, this would be sufficient for my problem. Thanks. I edited the question. | |
| Mar 11, 2021 at 8:01 | history | edited | ARedder | CC BY-SA 4.0 |
added 160 characters in body
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| Mar 11, 2021 at 0:44 | comment | added | Iosif Pinelis | It is unclear what you want to show. Is it the following: $\forall x\in\partial X\ \exists\epsilon>0\ \forall y\in X^c\ \|y-x\|<\epsilon\implies\nabla P(y)^T(x-y)<0$? Here $X:=\mathcal X$. Placing the quantifiers $\forall$ and $\exists$ correctly and unambiguously is usually very important. | |
| Mar 10, 2021 at 13:11 | comment | added | Hannes | Alright so a degree of explicitness is needed. I suppose you would need to assume some more on the function $P$ then. For instance, if you require the norm of $\nabla^2 P$ to be bounded on a neighborhood of $\mathcal{X}$, then you get a uniform estimate on the $o(\|x-y\|)$ term and this should lead to a more explicit result. | |
| Mar 10, 2021 at 12:51 | comment | added | ARedder | The problem is, the point where I have the descent direction is $z=y+\lambda(x-y)$. However, for my problem, I need that $z$ is a specified point or at least arbitrarily close to some other point $z'$ (we can use continuity), which we can make arbitrarily close to the boundary. | |
| Mar 10, 2021 at 12:35 | comment | added | Hannes | Why not the mean value theorem? For every $y \in \mathcal{X}^c$, there is $\lambda \in (0,1)$ such that $P(x) = 0 = P(y) + \nabla P(y + \lambda(x-y))^\top(x-y)$. Hence $x-y$ is a descent direction in the intermediate point $y + \lambda(x-y)$. | |
| Mar 10, 2021 at 12:09 | review | First posts | |||
| Mar 10, 2021 at 12:14 | |||||
| Mar 10, 2021 at 12:05 | comment | added | ARedder | I reposted this from math.stackexchange.com/posts/4055496/edit. I welcome suggestions to improve the title. Thanks. | |
| Mar 10, 2021 at 12:03 | history | asked | ARedder | CC BY-SA 4.0 |