Thread Subject: linear regression with a nonlinear constraint

I have a linear regression problem in which the variables
X,Y,Z are related by
 
Z=aX+bY+c

but a I have the nonlinear constraint c=a^2+b^2

Anybody can tell me how to solve this problem?

"Santiago Mazuelas" <mazuyo@hotmail.com> wrote in message
<fr6t5q$648$1@fred.mathworks.com>...
> I have a linear regression problem in which the variables
> X,Y,Z are related by
>
> Z=aX+bY+c
>
> but a I have the nonlinear constraint c=a^2+b^2
>
> Anybody can tell me how to solve this problem?

Hi

Try function LMFnlsq

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=17534&objectType=FILE

to obtain least squares solution by calling

res = @(ab) X*ab(1)+Y*ab(2)+ab(1)^2+ab(2)^2-Z;
x = LMFnlsq(res,x0);

where x0 is the inoitial guess of the solution, x(1)=a and
x(2)=b.

I hope it helps.

Mira

"Miroslav Balda" <balda.nospam@cdm.it.cas.cz> wrote in
message <fr7smj$ql9$1@fred.mathworks.com>...
> "Santiago Mazuelas" <mazuyo@hotmail.com> wrote in message
> <fr6t5q$648$1@fred.mathworks.com>...
> > I have a linear regression problem in which the
variables
> > X,Y,Z are related by
> >
> > Z=aX+bY+c
> >
> > but a I have the nonlinear constraint c=a^2+b^2
> >
> > Anybody can tell me how to solve this problem?
>
> Hi
>
> Try function LMFnlsq
>
>
http://www.mathworks.com/matlabcentral/fileexchange/loadFile
.do?objectId=17534&objectType=FILE
>
> to obtain least squares solution by calling
>
> res = @(ab) X*ab(1)+Y*ab(2)+ab(1)^2+ab(2)^2-Z;
> x = LMFnlsq(res,x0);
>
> where x0 is the inoitial guess of the solution, x(1)=a
and
> x(2)=b.
>
> I hope it helps.
>
> Mira
>
>
>

Ok but I want a solution that do not need a initial guess.
I realize that my problem is non linear indeed, but maybe
not too much non linear..

On 2008-03-12 05:33:01 -0400, "Santiago Mazuelas" <mazuyo@hotmail.com> said:
> Ok but I want a solution that do not need a initial guess.
> I realize that my problem is non linear indeed, but maybe
> not too much non linear..

Are you sure that's what you mean?

All numerical solvers require some sort of initial guess. Even if you
don't specify one, the solver is calculating its own initial guess.