Timeline for Does the Perron vector maximize $x^TAx$ in the simplex?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2019 at 0:46 | vote | accept | dineshdileep | ||
| Sep 19, 2019 at 0:20 | review | Close votes | |||
| Sep 25, 2019 at 23:35 | |||||
| S Sep 18, 2019 at 22:42 | history | suggested | Rodrigo de Azevedo |
Since no information is provided on the concavity of the objective, I would remove the convex optimization tag.
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| Sep 18, 2019 at 18:49 | review | Suggested edits | |||
| S Sep 18, 2019 at 22:42 | |||||
| Sep 18, 2019 at 18:34 | comment | added | Anthony Quas | @RodrigodeAzevedo: I see what you mean... | |
| Sep 18, 2019 at 16:27 | comment | added | Rodrigo de Azevedo | @AnthonyQuas Exactly. Even if it did, it's a maximization problem. Since there is no information on the concavity of $\bf x^\top A x$, I wonder whether the tag convex optimization is appropriate. Thus, my initial comment. | |
| Sep 18, 2019 at 8:38 | comment | added | Anthony Quas | No. The matrix {{1,1},{1,0}} is non-negative but not positive semi-definite (it has a negative determinant and so a negative eigenvalue. | |
| Sep 18, 2019 at 8:04 | comment | added | Rodrigo de Azevedo | @AnthonyQuas Does positivity imply positive definiteness? | |
| Sep 18, 2019 at 7:27 | comment | added | Anthony Quas | @RodrigodeAzevedo: There is optimization of a convex quantity over a convex region; therefore it's convex optimization | |
| Sep 18, 2019 at 6:12 | comment | added | Rodrigo de Azevedo | Then why the convex optimization tag if it is not convex? | |
| S Sep 18, 2019 at 6:04 | history | suggested | Rodrigo de Azevedo | CC BY-SA 4.0 |
Edited tags. Improved wording and formatting.
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| Sep 18, 2019 at 6:04 | comment | added | dineshdileep | It doesn't require convexity. | |
| Sep 18, 2019 at 6:00 | comment | added | Rodrigo de Azevedo | Why is this convex? | |
| Sep 18, 2019 at 5:59 | review | Suggested edits | |||
| S Sep 18, 2019 at 6:04 | |||||
| Sep 18, 2019 at 3:07 | comment | added | dineshdileep | @Pushpendre thanks!. In my case, the matrix is strictly positive ($A_{ij}>0$) and in fact, it is ok to assume that the matrix is positive definite. Examples pointed out in the answer as well as your comment are extremely sparse. I am wondering (and hoping) if that makes a difference | |
| Sep 18, 2019 at 2:30 | comment | added | Pushpendre | Just consider the identity matrix. Every feasible vector (feasible means satisfies the constraints) is also optimal for the first problem but it may not even be feasible for the second one. | |
| Sep 17, 2019 at 12:12 | comment | added | Alexandre Eremenko | In English, in such names as "Perron vector", the capital letter is used. | |
| Sep 17, 2019 at 1:28 | answer | added | Anthony Quas | timeline score: 7 | |
| Sep 17, 2019 at 0:40 | history | asked | dineshdileep | CC BY-SA 4.0 |