Timeline for matching two positive-semidefinite matrices
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2022 at 3:53 | vote | accept | John | ||
| Aug 28, 2022 at 3:52 | answer | added | Harry | timeline score: 5 | |
| Nov 23, 2018 at 22:12 | comment | added | Mahdi - Free Palestine | Yes. Indeed, A convex function (over a polytope) attains its maximum at an extreme point. | |
| Nov 23, 2018 at 21:59 | comment | added | John | @Mahdi, did you mean to get a continuous $P$ first via optimization, then make it discrete with {0,1} elements? | |
| Nov 23, 2018 at 21:54 | comment | added | Mahdi - Free Palestine | Yes, that was a typo. Since $\|Q_1^T P Q_2 \|_F$ is a convex function, the optimum value didn't change if we get optimum over the convex hull of all permutation matrices, which is equal to doubly stochastic matrices. I am not sure, is there any exact algorithm, for maximizing that quadratic function over some linear constraints. | |
| Nov 23, 2018 at 21:31 | comment | added | John | @Mahdi, I think you meant $Q_{ij}=b_ja_i^T$. So, we need to maximize $\sum_{1\le i,j,\le k}tr(PQ_{ij})^2$. Could you explain a little bit more to maximize it? Here, $P$ is a permutation matrix. | |
| Nov 22, 2018 at 18:17 | comment | added | Mahdi - Free Palestine | Also, we have $\|Q_1^T P Q_2 \|_F^2 = \sum_{1\leq i,j\leq k}(a_i^TPb_j)^2 = \sum_{1\leq i,j\leq k} \tr(PQ_{ij})^2 $, where $a_i$'s and $b_i$'s are respectively columns of $Q_1$ and $Q_2$ and $Q_{ij}=a_ib_j^T$. | |
| Nov 22, 2018 at 18:17 | comment | added | Mahdi - Free Palestine | As a cheap observation, we can equivalently maximize $\|Q_1^T P Q_2 \|_F$ over doubly stochastic matrices. | |
| Nov 22, 2018 at 5:57 | review | Suggested edits | |||
| Nov 22, 2018 at 11:22 | |||||
| Nov 21, 2018 at 21:28 | history | edited | John | CC BY-SA 4.0 |
added 98 characters in body
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| Nov 21, 2018 at 20:47 | history | asked | John | CC BY-SA 4.0 |