Timeline for Minimizing quadratic form over permutations
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2010 at 21:07 | history | edited | gondolier | CC BY-SA 2.5 |
added 1 characters in body
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| Aug 3, 2010 at 12:39 | history | edited | Charles Matthews | CC BY-SA 2.5 |
upper case title
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| Aug 3, 2010 at 6:26 | comment | added | gondolier | BTW, the x I am considering is a probability vector, or equivalently, $x \in \mathbb{R}_+^n$. | |
| Aug 3, 2010 at 6:25 | history | edited | gondolier | CC BY-SA 2.5 |
added 4 characters in body
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| Aug 3, 2010 at 6:24 | comment | added | gondolier | Sorry for the typo... 1's should be -1's. | |
| Aug 3, 2010 at 6:17 | comment | added | Tracy Hall | Did you mean for the example $Q$ to have its $1$'s on the antidiagonal, or to have $-1$'s, or for the optimization to seek the maximum? As stated, $Q$ fails for $x$ with two $0$'s and two $1$'s: the minimum is $0$, but sorting gives $2$. | |
| Aug 3, 2010 at 6:02 | comment | added | Tracy Hall | Unless there are more conditions on $x$, a necessary condition is that $Q$ be persymmetric (both equal to its transpose and unchanged when the order of the rows and order of the columns are reversed) since $x$ and $-x$ take the same value on the quadratic form but are sorted in opposite order. | |
| Aug 3, 2010 at 5:32 | history | asked | gondolier | CC BY-SA 2.5 |