Timeline for Eigenvalue problem with two quadratic constraints
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2017 at 3:54 | comment | added | Pushpendre | Your problem is a non-convex QCQP. If you don't need to code up the solution yourself, you could just use a general QCQP solver | |
| Nov 14, 2017 at 2:56 | comment | added | Yang | @fedja Thank you. That's a general way. I understand it better now - in terms of physical picture alas. | |
| Nov 13, 2017 at 2:29 | comment | added | fedja | It is concave, actually, so you can use the standard bisection techniques and find the maximum fairly quickly. | |
| Nov 13, 2017 at 1:25 | comment | added | fedja | And, yeah, symmetrize $B$ first; there is no need to keep it asymmetric. | |
| Nov 13, 2017 at 1:18 | comment | added | fedja | Well, let $x$ be a minimizer of $\langle(A+\mu B)x,x\rangle$ if $\langle Bx,x\rangle=0$, you are done. If not, you can change $\mu$ a little bit to move the minimum up (assuming you do not hit multiple eigenvalues, in which case you have to search for a vector satisfying the constraint in the full eigenspace). I have no idea how efficient that can be made (the trickery is to adjust $\mu$ neither too slow, nor too fast and the whole thing is just searching for the maximum of an expensive to compute function, so you'd better think of what you can say about that min as a function of $\mu$ first) | |
| Nov 12, 2017 at 21:33 | history | edited | Yang | CC BY-SA 3.0 |
improving narrative, adding background info.
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| Nov 12, 2017 at 15:54 | answer | added | Mark L. Stone | timeline score: 2 | |
| S Nov 12, 2017 at 9:56 | history | suggested | Rodrigo de Azevedo | CC BY-SA 3.0 |
The problem is non-convex
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| Nov 12, 2017 at 7:40 | review | Suggested edits | |||
| S Nov 12, 2017 at 9:56 | |||||
| Nov 12, 2017 at 5:04 | answer | added | Igor Rivin | timeline score: 3 | |
| Nov 12, 2017 at 4:45 | review | Close votes | |||
| Nov 12, 2017 at 13:45 | |||||
| Nov 12, 2017 at 3:09 | review | First posts | |||
| Nov 12, 2017 at 3:11 | |||||
| Nov 12, 2017 at 3:08 | history | asked | Yang | CC BY-SA 3.0 |