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Torsten
Posts:
1,684
Registered:
11/8/10


Re: constrained regression/optimization
Posted:
Feb 1, 2013 8:05 AM


"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 + (1a) * [Z + b*Q + (1b) * W] > > where: > >  X, Y, Z, Q and W are data vectors; >  constant should ideally be equal to zero (but this isn't necessary); >  1a, b and 1b 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=(1a)*b, your expression for X becomes X=c1*Y+(1c1)*Z+c2*Q+(1c1c2)*W. Thus you want to minimize the norm of c1*(YZW)+c2*(QW)+(Z+WX) under the constraints c1 >= 0 1c1 >= 0 c2 >= 0 1c1c2 >= 0
After solving the above problem, you can recover a and b via a=c1, b=c2/(1c1)
Best wishes Torsten.



