Thread Subject: question about constrained optimization

Hello everyone,

Happy 2008 to all of you!

I have a question about constrained optimization.

Say, my objective function is as follows:

f=x(1)^4-x(2)^2+x(3)^2-2*x(4)+x(2);

Now, I have the following constraints:

f = 0 when x(1) <= x(2)

and the above equation only holds when x(1) > x(2).

I guess the second constraint can be specified as an inequality
constraint. So:
ceq = x(1) - x(2); Is this correct?

Can someone tell me how I can specify the first constraint... saying
the function evaluates to 0 when x(1) <= x(2)?

Cheers,
Luca

luca.pamparana@gmail.com wrote in message
<d9f7479a-1137-4347-ba29-a27bad6d1eb9@l32g2000hse.googlegroups.com>...
> Hello everyone,
>
> Happy 2008 to all of you!
>
> I have a question about constrained optimization.
>
> Say, my objective function is as follows:
>
> f=x(1)^4-x(2)^2+x(3)^2-2*x(4)+x(2);
>
> Now, I have the following constraints:
>
> f = 0 when x(1) <= x(2)
>

To me, this does NOT describe a constraint in the sense
people know. You simply have a discontinuous function that
is defined differently in two sets of R^4.

Bruno

On Jan 4, 12:49 pm, "Bruno Luong" <b.lu...@fogale.fr> wrote:
> luca.pampar...@gmail.com wrote in message
>
> <d9f7479a-1137-4347-ba29-a27bad6d1...@l32g2000hse.googlegroups.com>...
>
> > Hello everyone,
>
> > Happy 2008 to all of you!
>
> > I have a question about constrained optimization.
>
> > Say, my objective function is as follows:
>
> > f=x(1)^4-x(2)^2+x(3)^2-2*x(4)+x(2);
>
> > Now, I have the following constraints:
>
> > f = 0 when x(1) <= x(2)
>
> To me, this does NOT describe a constraint in the sense
> people know. You simply have a discontinuous function that
> is defined differently in two sets of R^4.
>
> Bruno

Hello Bruno,

Thanks for the reply. You are obviously correct. I guess I only need
that one inequality constraint.

So, the constraint that x(1) > x(2) can be coded as:
ceq = x(1) - x(2); Is this correct?

Cheers,
Luca

luca.pamparana@gmail.com wrote in message <dcc7b5d9-3074-42e3-
98a6-1cb7a7e957f3@d21g2000prf.googlegroups.com>...
> On Jan 4, 12:49 pm, "Bruno Luong" <b.lu...@fogale.fr> wrote:
> > luca.pampar...@gmail.com wrote in message
> >
> > <d9f7479a-1137-4347-ba29-
a27bad6d1...@l32g2000hse.googlegroups.com>...
> >
> > > Hello everyone,
> >
> > > Happy 2008 to all of you!
> >
> > > I have a question about constrained optimization.
> >
> > > Say, my objective function is as follows:
> >
> > > f=x(1)^4-x(2)^2+x(3)^2-2*x(4)+x(2);
> >
> > > Now, I have the following constraints:
> >
> > > f = 0 when x(1) <= x(2)
> >
> > To me, this does NOT describe a constraint in the sense
> > people know. You simply have a discontinuous function that
> > is defined differently in two sets of R^4.
> >
> > Bruno
>
> Hello Bruno,
>
> Thanks for the reply. You are obviously correct. I guess I only need
> that one inequality constraint.
>
> So, the constraint that x(1) > x(2) can be coded as:
> ceq = x(1) - x(2); Is this correct?

Asuming that your comments imply the use
of fmincon, this is a LINEAR constraint. Why
not use the ability of fmincon to apply a linear
inequality constraint directly? Look at the A
and B arguments to fmincon. (The third and
4th args.)

If your function is truly discontinuous, an
optimizer like fmincon is not the correct tool
anyway, unless you do intend to constrain it
from looking in that part of the domain.

John

luca.pamparana@gmail.com wrote in message <dcc7b5d9-3074-
42e3-98a6-1cb7a7e957f3@d21g2000prf.googlegroups.com>...
> On Jan 4, 12:49 pm, "Bruno Luong" <b.lu...@fogale.fr>
wrote:
> > luca.pampar...@gmail.com wrote in message
> >
> > <d9f7479a-1137-4347-ba29-
a27bad6d1...@l32g2000hse.googlegroups.com>...
> >
> > > Hello everyone,
> >
> > > Happy 2008 to all of you!
> >
> > > I have a question about constrained optimization.
> >
> > > Say, my objective function is as follows:
> >
> > > f=x(1)^4-x(2)^2+x(3)^2-2*x(4)+x(2);
> >
> > > Now, I have the following constraints:
> >
> > > f = 0 when x(1) <= x(2)
> >
> > To me, this does NOT describe a constraint in the sense
> > people know. You simply have a discontinuous function
that
> > is defined differently in two sets of R^4.
> >
> > Bruno
>
> Hello Bruno,
>
> Thanks for the reply. You are obviously correct. I guess
I only need
> that one inequality constraint.
>
> So, the constraint that x(1) > x(2) can be coded as:
> ceq = x(1) - x(2); Is this correct?
>
> Cheers,
> Luca
>

Luca,

I'm looking at this, and am still a little confused as to
what you need. Are trying to find a minimum (or maximum)
of the f that you've given, subject to a constraint? Or
are you trying to solve f = 0 subject to a constraint?

Also, is this the actual function you're interested in, or
is it an example to illustrate your problem? I ask,
because if your intention is to find a max or min of the
given f, it's extremely simply to do so by hand, without
having to use Matlab.

Charles.

On Jan 4, 6:45 pm, "Charles Cuell" <cu...@math.usask.ca> wrote:
> luca.pampar...@gmail.com wrote in message <dcc7b5d9-3074-
>
> 42e3-98a6-1cb7a7e95...@d21g2000prf.googlegroups.com>...> On Jan 4, 12:49 pm, "Bruno Luong" <b.lu...@fogale.fr>
> wrote:
> > > luca.pampar...@gmail.com wrote in message
>
> > > <d9f7479a-1137-4347-ba29-
>
> a27bad6d1...@l32g2000hse.googlegroups.com>...
>
>
>
>
>
> > > > Hello everyone,
>
> > > > Happy 2008 to all of you!
>
> > > > I have a question about constrained optimization.
>
> > > > Say, my objective function is as follows:
>
> > > > f=x(1)^4-x(2)^2+x(3)^2-2*x(4)+x(2);
>
> > > > Now, I have the following constraints:
>
> > > > f = 0 when x(1) <= x(2)
>
> > > To me, this does NOT describe a constraint in the sense
> > > people know. You simply have a discontinuous function
> that
> > > is defined differently in two sets of R^4.
>
> > > Bruno
>
> > Hello Bruno,
>
> > Thanks for the reply. You are obviously correct. I guess
> I only need
> > that one inequality constraint.
>
> > So, the constraint that x(1) > x(2) can be coded as:
> > ceq = x(1) - x(2); Is this correct?
>
> > Cheers,
> > Luca
>
> Luca,
>
> I'm looking at this, and am still a little confused as to
> what you need. Are trying to find a minimum (or maximum)
> of the f that you've given, subject to a constraint? Or
> are you trying to solve f = 0 subject to a constraint?
>
> Also, is this the actual function you're interested in, or
> is it an example to illustrate your problem? I ask,
> because if your intention is to find a max or min of the
> given f, it's extremely simply to do so by hand, without
> having to use Matlab.
>
> Charles.

Hey Charles,

Thanks for the reply.

The function that I gave was just meant to serve as an example. My
real function is a set of observations measured at different times
which should follow a certain model. However, of course because of
noise and all that I have to do this regression.

Cheers,
Luca