Timeline for Optimization with matrix determinant as constraint
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2017 at 17:17 | comment | added | Maghoumi | @FeiZhu Did you ever solve this problem? | |
| Jun 30, 2015 at 5:23 | comment | added | Fei Zhu | Generally no more than 20. | |
| Jun 28, 2015 at 6:47 | history | tweeted | twitter.com/#!/StackSciComp/status/615048957866213376 | ||
| Jun 28, 2015 at 4:22 | comment | added | hardmath♦ | How many $\mathbf{E_i}$ vectors are involved? | |
| Jun 27, 2015 at 9:11 | history | edited | Fei Zhu | CC BY-SA 3.0 |
provide form of the objective function and other constraints
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| Jun 26, 2015 at 14:10 | answer | added | Mark L. Stone | timeline score: 3 | |
| Jun 5, 2015 at 16:49 | comment | added | hardmath♦ | The constraint $\det A \gt 0$ is very mild. It would be helpful to know what objective function is being optimized and all the constraints so that suggestions can be more targeted. | |
| Jun 5, 2015 at 2:24 | comment | added | Fei Zhu | Indeed the gradient is numerically unstable and that's why I'm seraching for a solution that avoids naively computing the unstable gradient. $\mathbf{A}$ is 6$\times$6 in our case, and the objective is quadratic with respect to $\mathbf{A}$. | |
| Jun 4, 2015 at 20:57 | comment | added | Stefano M | Your formula ${\partial \mathrm{det}(\mathbf{A})}/{\partial \mathbf{A}} = \mathrm{det}(\mathbf{A})(\mathbf{A}^{-1})^T$ is numerically unstable when $\mathrm{det}(\mathbf{A})=0$: you are trying to express a finite quantity as $0\cdot\infty$, and this is not possible by naively computing the product of a small term times a very big (ill conditioned) one. Apart from the very pertinent answer by @ArnoldNeumaier, other computing strategies could be devised, if you provide some more background. How big is $\mathbf{A}$, are you trying a global or a local optimisation? | |
| Jun 4, 2015 at 15:46 | answer | added | Arnold Neumaier | timeline score: 4 | |
| Jun 4, 2015 at 8:34 | history | asked | Fei Zhu | CC BY-SA 3.0 |