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Torsten
Posts:
1,133
Registered:
11/8/10
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Re: constrained regression/optimization
Posted:
Feb 1, 2013 8:05 AM
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"Jelena Ivanovic" <ivanovic.jelena@yahoo.com> wrote in message <keefrt$m0f$1@newscl01ah.mathworks.com>...
> Dear all,
>
> I am relatively new Matlab user, and I need to find a solution for coefficients a and b in the following equation:
>
> X=a*Y + (1-a) * [Z + b*Q + (1-b) * W]
>
> where:
>
> - X, Y, Z, Q and W are data vectors;
> - constant should ideally be equal to zero (but this isn't necessary);
> - 1-a, b and 1-b all need to be positive.
>
> Is there maybe something that could be done with lsqlin from the Optimization toolbox?
>
> Many thanks,
>
> Jelena
Setting
c1=a and c2=(1-a)*b,
your expression for X becomes
X=c1*Y+(1-c1)*Z+c2*Q+(1-c1-c2)*W.
Thus you want to minimize the norm of
c1*(Y-Z-W)+c2*(Q-W)+(Z+W-X)
under the constraints
c1 >= 0
1-c1 >= 0
c2 >= 0
1-c1-c2 >= 0
After solving the above problem, you can recover a and b via
a=c1, b=c2/(1-c1)
Best wishes
Torsten.
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