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Thread Subject:
Fmincon and eigenvector corresponding to minimum eigen value

Subject: Fmincon and eigenvector corresponding to minimum eigen value

From: Dinesh Bhati

Date: 25 Aug, 2011 06:14:29

Message: 1 of 7

Hi,

Is it true that fmincon solution is the eigenvector corresponding to the smallest eigen value of the objective function

phi=b'*R*b;

Thanks
Dinesh

Subject: Fmincon and eigenvector corresponding to minimum eigen value

From: Torsten

Date: 25 Aug, 2011 06:28:01

Message: 2 of 7

On 25 Aug., 08:14, "Dinesh Bhati" <bhatidin...@gmail.com> wrote:
> Hi,
>
> Is it true that fmincon solution is the eigenvector corresponding to the smallest eigen value of the objective function
>
> phi=b'*R*b;
>
> Thanks
> Dinesh

If ||b||_2 is constrained to be <= a positive constant C (e.g. C=1),
then the solution b is the eigenvector
corresponding to the smallest eigenvalue of the matrix 0.5*(R+R').

Best wishes
Torsten.

Subject: Fmincon and eigenvector corresponding to minimum eigen value

From: Dinesh Bhati

Date: 25 Aug, 2011 06:53:08

Message: 3 of 7

Thanks for your interest Torsten.May I know What is the best way to minimize phi w.r.t the variable 'x' in the following case

b=f(x)
c=f(x)
phi=x'*R*x+b'*R*b+c'*R*c

Please tell me some methods.

Thanks
Dinesh



Torsten <Torsten.Hennig@umsicht.fraunhofer.de> wrote in message <e36095f4-c44a-4292-b1c2-30e516f41438@c29g2000yqd.googlegroups.com>...
> On 25 Aug., 08:14, "Dinesh Bhati" <bhatidin...@gmail.com> wrote:
> > Hi,
> >
> > Is it true that fmincon solution is the eigenvector corresponding to the smallest eigen value of the objective function
> >
> > phi=b'*R*b;
> >
> > Thanks
> > Dinesh
>
> If ||b||_2 is constrained to be <= a positive constant C (e.g. C=1),
> then the solution b is the eigenvector
> corresponding to the smallest eigenvalue of the matrix 0.5*(R+R').
>
> Best wishes
> Torsten.

Subject: Fmincon and eigenvector corresponding to minimum eigen value

From: Torsten

Date: 25 Aug, 2011 08:38:41

Message: 4 of 7

On 25 Aug., 08:53, "Dinesh Bhati" <bhatidin...@gmail.com> wrote:
> Thanks for your interest Torsten.May I know What is the best way to minimize phi w.r.t the variable 'x' in the following case
>
> b=f(x)
> c=f(x)
> phi=x'*R*x+b'*R*b+c'*R*c
>
> Please tell me some methods.
>
> Thanks
> Dinesh
>
>
>
> Torsten <Torsten.Hen...@umsicht.fraunhofer.de> wrote in message <e36095f4-c44a-4292-b1c2-30e516f41...@c29g2000yqd.googlegroups.com>...
> > On 25 Aug., 08:14, "Dinesh Bhati" <bhatidin...@gmail.com> wrote:
> > > Hi,
>
> > > Is it true that fmincon solution is the eigenvector corresponding to the smallest eigen value of the objective function
>
> > > phi=b'*R*b;
>
> > > Thanks
> > > Dinesh
>
> > If ||b||_2 is constrained to be <= a positive constant C (e.g. C=1),
> > then the solution b is the eigenvector
> > corresponding to the smallest eigenvalue of the matrix 0.5*(R+R').
>
> > Best wishes
> > Torsten.- Zitierten Text ausblenden -
>
> - Zitierten Text anzeigen -

It depends on how complicated the functions b=f1(x) and c=f2(x) look
like
and what constraints you want to set on x.

Best wishes
Torsten.

Subject: Fmincon and eigenvector corresponding to minimum eigen value

From: Bruno Luong

Date: 25 Aug, 2011 08:55:32

Message: 5 of 7

"Dinesh Bhati" <bhatidinesh@gmail.com> wrote in message <j34rgk$2k8$1@newscl01ah.mathworks.com>...
> Thanks for your interest Torsten.May I know What is the best way to minimize phi w.r.t the variable 'x' in the following case
>
> b=f(x)
> c=f(x)
> phi=x'*R*x+b'*R*b+c'*R*c
>
> Please tell me some methods.

I propose to look at Gauss-Newton method.

Bruno

Subject: Fmincon and eigenvector corresponding to minimum eigen value

From: Dinesh Bhati

Date: 25 Aug, 2011 09:12:10

Message: 6 of 7

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <j352m4$lu5$1@newscl01ah.mathworks.com>...
> "Dinesh Bhati" <bhatidinesh@gmail.com> wrote in message <j34rgk$2k8$1@newscl01ah.mathworks.com>...
> > Thanks for your interest Torsten.May I know What is the best way to minimize phi w.r.t the variable 'x' in the following case
> >
> > b=f(x)
> > c=f(x)
> > phi=x'*R*x+b'*R*b+c'*R*c
> >
> > Please tell me some methods.
>
> I propose to look at Gauss-Newton method.

How fmincon and Gauss-Newton are different.?Can you give some hints.
Dinesh

Subject: Fmincon and eigenvector corresponding to minimum eigen value

From: Bruno Luong

Date: 25 Aug, 2011 09:31:11

Message: 7 of 7

>
> How fmincon and Gauss-Newton are different.?

To know about the difference between numerical methods, you should read the reference papers cited in the bottom of the doc of FMINCON, and textbook for Gauss-Newton method.

The advantage of Gauss-Newton in your case is that you can easily compute the quadratic form at each iteration providing the Jacobian of two non-linear functions f_b and f_c. The quadratic form can be minimized by standard linear matrix algebra.

FMINCON - a generic tool - has no way to exploit intelligently the form of your objective function as I just explain.

Bruno

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