Timeline for Detecting non-negativity of a single constraint by polyhedral constraints - $I$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2021 at 11:02 | vote | accept | Turbo | ||
| May 11, 2021 at 11:02 | |||||
| May 11, 2021 at 11:02 | vote | accept | Turbo | ||
| May 11, 2021 at 11:02 | |||||
| May 11, 2021 at 11:00 | comment | added | Dima Pasechnik | you implicitly assume that $a\geq 0$ and $b\geq 0$, and this implies that $x$ exists. You eight drop this, then your question might make sense, or you insist on this, and then I have given you the answer. | |
| May 11, 2021 at 1:46 | comment | added | Turbo | I don't see how 0<=1 implies there is a non-negative x. It means there is always a non-negative x satisfying an equality relation which is false. I don't understand the meaning you are trying to convey. I am looking for a simple argument we cannot reduce the problem to membership in polyhedron. I think your answers do not cut it. | |
| May 10, 2021 at 19:17 | comment | added | Turbo | So implies version is trivial. If I ask $\iff$ is there possibility? | |
| May 10, 2021 at 18:47 | comment | added | Dima Pasechnik | surely, e.g. B=0, c=1. | |
| May 10, 2021 at 15:51 | comment | added | Turbo | So there is a $B$? | |
| May 10, 2021 at 15:33 | comment | added | Dima Pasechnik | Any $B, c$ so that the corr. system of inequalities holds for any $a\geq 0$, $b\geq 0$ will do. These $B, c$ all describe the same polyhedron, the positive ortant. | |
| May 10, 2021 at 14:21 | comment | added | Turbo | I think I can sense it but I do not see it. | |
| May 10, 2021 at 14:04 | comment | added | Dima Pasechnik | anything that only depend on an individual equation will not work, and your B is like this. | |
| May 10, 2021 at 13:52 | comment | added | Turbo | I am looking for a formal proof no polyhedra involving $B$ exists and it is likely a simple convexity argument and I am missing it. 'I don't think' is not convincing. | |
| May 10, 2021 at 12:50 | history | answered | Dima Pasechnik | CC BY-SA 4.0 |