Optimal selection from function set. A selection matrix is calculated by optimizing the constrain objective function.
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There are four functions, expressed as
,i=1,2,...,I, and where u=[-1 1],(code in [-1:0.01:1]),I=4,
{0.1 0.11 0.12 0.13}.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795909/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795919/image.png)
Define another function
, p=1,2,...,P, P=64 and
is a random number between [0.4 0.5].
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795924/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795929/image.png)
The question is how to choice a
in each p to achive the objective function
where
[-1,0] and
[0.15 1],
is one of {
}.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795934/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795939/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795944/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795944/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795954/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795959/image.png)
The output can be a matrix
in which only one element in each row is 1 and the rest are 0, that is, if
=1, the ith function is selected for the pth calculation.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795964/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795969/image.png)
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