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Thread Subject:
Solve non linear constraint optimization

Subject: Solve non linear constraint optimization

From: fas

Date: 24 Jan, 2009 01:58:02

Message: 1 of 5

I want to minimize this constraint least square to find a and b. Had
it be a linear system it would be probably easy to solve this
constraint problem. But I have this function of non linear equations
to solve.
f=sum[x*x']*[a,b,b^2/(4*a)]' - sum[y*x] +lambda*[-b^2/(4*a^2), (1/2)*
(b/a),-1]'=0
Here x,y are vectors in R3 and sum is over i to n;
Can anyone help me solve this optimization.

Subject: Solve non linear constraint optimization

From: Matt

Date: 24 Jan, 2009 14:49:02

Message: 2 of 5

fas <faisalmufti@gmail.com> wrote in message <9dc7b2b2-6103-47dc-a474-c7fda15518c8@t26g2000prh.googlegroups.com>...
> I want to minimize this constraint least square to find a and b. Had
> it be a linear system it would be probably easy to solve this
> constraint problem. But I have this function of non linear equations
> to solve.
> f=sum[x*x']*[a,b,b^2/(4*a)]' - sum[y*x] +lambda*[-b^2/(4*a^2), (1/2)*
> (b/a),-1]'=0
> Here x,y are vectors in R3 and sum is over i to n;
> Can anyone help me solve this optimization.

Probably not, since you've told us neither what the objective function is, nor the constraint.

It looks like you've given us Euler's equation above, but it will not be enough. We will need at minimum to know the constraint equation as well.

Subject: Solve non linear constraint optimization

From: fas

Date: 24 Jan, 2009 22:50:21

Message: 3 of 5

On Jan 25, 1:49=A0am, "Matt " <mjacobson.removet...@xorantech.com>
wrote:
> fas <faisalmu...@gmail.com> wrote in message <9dc7b2b2-6103-47dc-a474-c7f=
da1551...@t26g2000prh.googlegroups.com>...
> > I want to minimize this constraint least square to find a and b. Had
> > it be a linear system it would be probably easy to solve this
> > constraint problem. =A0But I have this function of non linear equations
> > to solve.
> > f=3Dsum[x*x']*[a,b,b^2/(4*a)]' - sum[y*x] +lambda*[-b^2/(4*a^2), (1/2)*
> > (b/a),-1]'=3D0
> > Here x,y are vectors in R3 =A0and sum is over i to n;
> > Can anyone help me solve this optimization.
>
> Probably not, since you've told us neither what the objective function is=
, nor the constraint.
>
> It looks like you've given us Euler's equation above, but it will not be =
enough. We will need at minimum to know the

The constraint in this case is b^2/(4*a)=3Dconstant.
It is some what similar to the case of first example of Lagranage
multipliers at
http://en.wikipedia.org/wiki/Lagrange_multipliers
where the third equation is non linear.

Subject: Solve non linear constraint optimization

From: Matt

Date: 24 Jan, 2009 23:32:01

Message: 4 of 5

fas <faisalmufti@gmail.com> wrote in message <6d9101fd-1d79-4642-85a0-4a12ba228829@v18g2000pro.googlegroups.com>...
> On Jan 25, 1:49=A0am, "Matt " <mjacobson.removet...@xorantech.com>
> wrote:
> > fas <faisalmu...@gmail.com> wrote in message <9dc7b2b2-6103-47dc-a474-c7f=
> da1551...@t26g2000prh.googlegroups.com>...
> > > I want to minimize this constraint least square to find a and b. Had
> > > it be a linear system it would be probably easy to solve this
> > > constraint problem. =A0But I have this function of non linear equations
> > > to solve.
> > > f=3Dsum[x*x']*[a,b,b^2/(4*a)]' - sum[y*x] +lambda*[-b^2/(4*a^2), (1/2)*
> > > (b/a),-1]'=3D0
> > > Here x,y are vectors in R3 =A0and sum is over i to n;
> > > Can anyone help me solve this optimization.
> >
> > Probably not, since you've told us neither what the objective function is=
> , nor the constraint.
> >
> > It looks like you've given us Euler's equation above, but it will not be =
> enough. We will need at minimum to know the
>
> The constraint in this case is b^2/(4*a)=3Dconstant.
> It is some what similar to the case of first example of Lagranage
> multipliers at
> http://en.wikipedia.org/wiki/Lagrange_multipliers
> where the third equation is non linear.

I don't think we're going to be able to help you without the original problem spelled out in full.

Subject: Solve non linear constraint optimization

From: Miroslav Balda

Date: 25 Jan, 2009 21:33:03

Message: 5 of 5

fas <faisalmufti@gmail.com> wrote in message <6d9101fd-1d79-4642-85a0-4a12ba228829@v18g2000pro.googlegroups.com>...
> On Jan 25, 1:49=A0am, "Matt " <mjacobson.removet...@xorantech.com>
> wrote:
> > fas <faisalmu...@gmail.com> wrote in message <9dc7b2b2-6103-47dc-a474-c7f=
> da1551...@t26g2000prh.googlegroups.com>...
> > > I want to minimize this constraint least square to find a and b. Had
> > > it be a linear system it would be probably easy to solve this
> > > constraint problem. =A0But I have this function of non linear equations
> > > to solve.
> > > f=3Dsum[x*x']*[a,b,b^2/(4*a)]' - sum[y*x] +lambda*[-b^2/(4*a^2), (1/2)*
> > > (b/a),-1]'=3D0
> > > Here x,y are vectors in R3 =A0and sum is over i to n;
> > > Can anyone help me solve this optimization.
> >
> > Probably not, since you've told us neither what the objective function is=
> , nor the constraint.
> >
> > It looks like you've given us Euler's equation above, but it will not be =
> enough. We will need at minimum to know the
>
> The constraint in this case is b^2/(4*a)=3Dconstant.
> It is some what similar to the case of first example of Lagranage
> multipliers at
> http://en.wikipedia.org/wiki/Lagrange_multipliers
> where the third equation is non linear.

Hello,
I think that the solution can be found by the least squares problem solution defined as a system of 4 equations for row vectors x and y
     xx = x*x';
     yx = y*x'; % I think that transposition by x has been vergotten
     res = @(z) [xx*[z(1); z(2); z(2)^2/(4*z(1))] - yx + ...
                      lambda*[-z(2)^2/(4*z(1)^2); (1/2)*(z(2)/z(1));-1]
                       z(2)^2 - (4*z(1))*constant];
     [z, ssq, cnt] = LMFnlsq(res,z0); % see FEX Id 17534
     a = z(1);
     b = z(2);
Hope it helps.
Best regards
Mira

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