Timeline for (probably simple) optimization question
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 28, 2012 at 18:42 | comment | added | Noah Stein | Could you explain how the first sentence of my previous comment does not answer your most recent update? | |
| Aug 28, 2012 at 17:34 | history | edited | Felix Goldberg | CC BY-SA 3.0 |
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| Aug 28, 2012 at 14:00 | comment | added | Suvrit | Yep: suppose $A$ is a diagonal matrix with $-1$ as its 1st entry, and all other entries zero. Then, clearly let $X=tI$, with $t\to \infty$ makes the problem unbounded below, and there is no minimum. The infimum is $-\infty$. So the problem needs either a compact set or some other modifications before it is well-posed. | |
| Aug 28, 2012 at 12:26 | comment | added | Noah Stein | If I understand the problem correctly, can't you minimize $(AX)_{ii}$ over the psd cone for each $i$ individually and then take the $i$ which makes this smallest? Of course, since the set of psd matrices is a cone and scaling $X$ scales your objective, you will either get an optimal value of $0$ achieved at $0$ (or as you approach $0$ if you are interested in the infimum and not including zero) or else the infimum will be $-\infty$. | |
| Aug 28, 2012 at 11:43 | history | edited | Felix Goldberg | CC BY-SA 3.0 |
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| Aug 28, 2012 at 11:37 | comment | added | Suvrit | Since it is in general NP-hard, it is of value to look at the specific case that you might have; perhaps that may be amenable to a global solution, or at least a good approximation algorithm....(if the solution exists at all) | |
| Aug 28, 2012 at 11:33 | comment | added | Felix Goldberg | Yes, I understand it'd be hard:) That's why i want to know if there are some approaches people have developed to this kind of problem. Thanks! | |
| Aug 28, 2012 at 11:33 | answer | added | none | timeline score: -1 | |
| Aug 28, 2012 at 11:28 | comment | added | Suvrit | it would be beneficial to see the explicit formulation. But since you are trying to minimize a concave function it won't be that easy.... | |
| Aug 28, 2012 at 11:03 | history | asked | Felix Goldberg | CC BY-SA 3.0 |