Timeline for Constrained Optimization Closed Form Solution Using KKT Gives Wrong Values
Current License: CC BY-SA 4.0
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| Nov 22, 2022 at 4:53 | answer | added | xd y | timeline score: 3 | |
| Nov 20, 2022 at 11:33 | comment | added | Charlie Vanaret | @IbrahimAmer: yeah, with nonnegativity bounds, hard to know which ones will be (in)active at the solution. But you could call a QP solver to solve this for you :) | |
| Nov 20, 2022 at 0:35 | comment | added | Ibrahim Amer | @cvanaret You are right! Thank you for your help! Now I guess the problem is solved but, another problem arouse here is when some of the decision variable can have negative values. I can add constraints to enforce $\gamma_j$ to be positive but that would make the closed-form solution impossible to attain | |
| Nov 20, 2022 at 0:07 | comment | added | Charlie Vanaret | @IbrahimAmer: in your Matlab code, there's a factor 2 missing in the definition of lambda_1, right? | |
| Nov 19, 2022 at 22:30 | history | edited | Ibrahim Amer | CC BY-SA 4.0 |
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| Nov 19, 2022 at 22:22 | comment | added | Ibrahim Amer | @cvanaret I have shared the full matlab code and the full notes for the solution. | |
| Nov 19, 2022 at 22:16 | history | edited | Ibrahim Amer | CC BY-SA 4.0 |
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| Nov 19, 2022 at 21:50 | comment | added | Ibrahim Amer | @cvanaret Thank you for your reply. Is it Okay to share the full solution with you via an iPad-written pdf solution document? | |
| Nov 19, 2022 at 21:49 | comment | added | Ibrahim Amer | @joni You are right. But I guess in this case it doesn't matter because the way a problem is solved using strict inequality constraints is the same, we just need to drop the strict constraint and make it $0 \leq \sum^m_{j=1} \gamma_j$. | |
| Nov 19, 2022 at 18:08 | comment | added | Charlie Vanaret | @joni If you're sure that the sum of the $\gamma_j$ is positive, you can just drop the lower bound. Ibrahim: I get the same value for $\lambda$. Can you share the full model/the code? | |
| Nov 19, 2022 at 9:48 | comment | added | joni | The KKT conditions don't hold for strict inequality constraints like $0 < \sum_{j=1}^{m} \gamma_j$. | |
| Nov 19, 2022 at 6:20 | history | edited | Ibrahim Amer | CC BY-SA 4.0 |
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| Nov 19, 2022 at 5:53 | history | edited | Ibrahim Amer | CC BY-SA 4.0 |
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| Nov 19, 2022 at 5:11 | history | edited | Ibrahim Amer | CC BY-SA 4.0 |
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| Nov 18, 2022 at 21:05 | history | edited | Ibrahim Amer | CC BY-SA 4.0 |
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| Nov 18, 2022 at 20:29 | history | asked | Ibrahim Amer | CC BY-SA 4.0 |