Timeline for Maximizing variance of bounded random variable through convex optimization
Current License: CC BY-SA 4.0
20 events
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| Jul 19, 2020 at 20:40 | history | edited | Boby | CC BY-SA 4.0 |
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| Jul 19, 2020 at 20:38 | comment | added | Boby | @J. Basically your approach counts the number of zeros of $q(X)$. Since there are at most two zeros, the result follows. My question then is: This is essentially all we can do with these equations just count zeros? Or is there some inversion that is possible? | |
| Jul 19, 2020 at 20:21 | comment | added | Boby | @J. Thanks. This is nice. Also, yes, less hands-on would be good. I want to use this optimization problem as an introductory example to convex optimization over p.d. spaces. Therefore, it would be good to use things that are less hands-on and easily generalize. | |
| Jul 19, 2020 at 19:59 | comment | added | Alf | The second KKT condition implies that there exists a nontrivial quadratic function $q$ such that $q(X) = 0$ almost surely. Therefore $P_X$ is supported on at most 2 points, and by the first equation these must be 0 and 1. The second equation then yields that indeed he made must be balanced. Or are you looking for something less hands on than this? | |
| Jul 19, 2020 at 16:10 | history | edited | Boby | CC BY-SA 4.0 |
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| Jul 19, 2020 at 13:13 | history | edited | Boby | CC BY-SA 4.0 |
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| Jul 19, 2020 at 13:13 | comment | added | Boby | @Dirk Yes, there should be an inequality outside of support. I will correct it. I would be very interested in looking at a dual approach, so if you have time please add some details or thoughts on how in. | |
| Jul 19, 2020 at 12:34 | comment | added | Dirk | I think that duality may help here. The (pre-)dual should be a convex minimization problem on the space of continuous functions. But I didn't think any further than that... On a second thought: I think that optimality conditions should say a bit more, namely that you have equality only on the support (i.e. the inequality is strict outside the support). | |
| Jul 19, 2020 at 11:35 | history | edited | Rodrigo de Azevedo | CC BY-SA 4.0 |
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| Jul 19, 2020 at 11:24 | history | edited | Boby | CC BY-SA 4.0 |
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| Jul 19, 2020 at 11:24 | comment | added | Boby | @RodrigodeAzevedo It's in a bullet point 1). I will clarify this. | |
| Jul 19, 2020 at 11:22 | history | edited | Boby | CC BY-SA 4.0 |
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| Jul 19, 2020 at 11:13 | history | edited | Boby | CC BY-SA 4.0 |
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| Jul 19, 2020 at 11:11 | history | edited | Boby | CC BY-SA 4.0 |
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| Jul 19, 2020 at 7:01 | review | Close votes | |||
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| Jul 19, 2020 at 1:46 | history | edited | YCor | CC BY-SA 4.0 |
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| Jul 19, 2020 at 1:37 | history | edited | Boby | CC BY-SA 4.0 |
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| S Jul 19, 2020 at 1:36 | history | suggested | RobPratt | CC BY-SA 4.0 |
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| Jul 19, 2020 at 1:36 | review | Suggested edits | |||
| S Jul 19, 2020 at 1:36 | |||||
| Jul 19, 2020 at 1:29 | history | asked | Boby | CC BY-SA 4.0 |