MATLAB Central Newsreader - linear regression with a nonlinear constraint

linear regression with a nonlinear constraint

Santiago Mazuelas — Tue, 11 Mar 2008 21:22:02 -0400

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?

Re: linear regression with a nonlinear constraint

Miroslav Balda — Wed, 12 Mar 2008 06:20:03 -0400

"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

Re: linear regression with a nonlinear constraint

Santiago Mazuelas — Wed, 12 Mar 2008 09:33:01 -0400

"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..

Re: linear regression with a nonlinear constraint

Arthur G — Wed, 12 Mar 2008 14:29:21 -0400

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.