Timeline for Matrix decomposition problem
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 8, 2010 at 4:18 | comment | added | Will Jagy | So put the cost 1 for $i \neq j$ but 0 for $i = j.$ | |
| Apr 7, 2010 at 18:49 | comment | added | silvanmx | Will, your cost function works but I found it hard to justify. A maximal trace has more meaning for my application as it implies a minimum change, etc. So, the problem can be stated as: Maximize $tr(C)$ subject to $C1=1$, $C^T1=1$ and $C>0$. I am just wondering if this problem accepts a unique solution or if there is an analytic solution out there. | |
| Apr 6, 2010 at 18:13 | comment | added | Will Jagy | Fine. I have three books titled Operations Research. Each calls this the Transportation Problem, while one adds in the adjective "balanced" in your case. Just put in a cost of $(i-j)^2$ at position $i,j$. My $c_{ij} = x_i y_j / M$ gives an initial feasible solution. | |
| Apr 6, 2010 at 15:08 | vote | accept | silvanmx | ||
| Apr 6, 2010 at 15:07 | vote | accept | silvanmx | ||
| Apr 6, 2010 at 15:08 | |||||
| Apr 6, 2010 at 15:02 | comment | added | silvanmx | Interesting! It seems my problem now reduces to find an appropriate cost function. | |
| Apr 6, 2010 at 15:01 | vote | accept | silvanmx | ||
| Apr 6, 2010 at 15:04 | |||||
| Apr 5, 2010 at 22:47 | history | answered | fedja | CC BY-SA 2.5 |