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From: Tiam on 24 Jan 2010 23:40
how would i set the conditions in fmincon using linear/nonlinear constraints, or UB and LB conditions, so that fmincon searches for the optimum values of x, within say -4~-7, or 4~7?

thanks in advance,
From: Matt J on 24 Jan 2010 23:55
"Tiam " <tiamz84(a)gmail.com> wrote in message <hjj7b4$i7s$1(a)fred.mathworks.com>...
> how would i set the conditions in fmincon using linear/nonlinear constraints, or UB and LB conditions, so that fmincon searches for the optimum values of x, within say -4~-7, or 4~7?

You mean you want to constraint to the union of the intervals [-7,-4] and [4,7] ?

Perhaps the nonlinear constraint

( x^2 - 5.5^2 ) ^2 <= 7^2 - 4^2
From: Bruno Luong on 25 Jan 2010 02:32
"Matt J " <mattjacREMOVE(a)THISieee.spam> wrote in message <hjj878$d4o$1(a)fred.mathworks.com>...
> "Tiam " <tiamz84(a)gmail.com> wrote in message <hjj7b4$i7s$1(a)fred.mathworks.com>...
> > how would i set the conditions in fmincon using linear/nonlinear constraints, or UB and LB conditions, so that fmincon searches for the optimum values of x, within say -4~-7, or 4~7?
>
> You mean you want to constraint to the union of the intervals [-7,-4] and [4,7] ?
>
> Perhaps the nonlinear constraint
>
> ( x^2 - 5.5^2 ) ^2 <= 7^2 - 4^2

Bad idea, the domains are composed by two disconnected sets. Depending where the starting point is located, FMINCON will find the (local) minimum is the associated domain. Re-parametrize does not solve the composite nature of the problem.

The only way is to optimize twice, one on each domain then compare the results.

Bruno
From: Matt J on 25 Jan 2010 10:07
"Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hjjhdi$t0d$1(a)fred.mathworks.com>...

> > Perhaps the nonlinear constraint
> >
> > ( x^2 - 5.5^2 ) ^2 <= 7^2 - 4^2
>
> Bad idea, the domains are composed by two disconnected sets. Depending where the starting point is located, FMINCON will find the (local) minimum is the associated domain. Re-parametrize does not solve the composite nature of the problem.
>
> The only way is to optimize twice, one on each domain then compare the results.

I see what you mean. Still, I wonder if it's not worthwhile if only because it expresses two bound constraints as 1 and therefore reduces the number of Lagrange multipliers that fmincon has to deal with. Then again, if that were true, I guess no one would ever use bound constraints...
From: John D'Errico on 25 Jan 2010 10:43
"Matt J " <mattjacREMOVE(a)THISieee.spam> wrote in message <hjkc2m$d1l$1(a)fred.mathworks.com>...
> "Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hjjhdi$t0d$1(a)fred.mathworks.com>...
>
> > > Perhaps the nonlinear constraint
> > >
> > > ( x^2 - 5.5^2 ) ^2 <= 7^2 - 4^2
> >
> > Bad idea, the domains are composed by two disconnected sets. Depending where the starting point is located, FMINCON will find the (local) minimum is the associated domain. Re-parametrize does not solve the composite nature of the problem.
> >
> > The only way is to optimize twice, one on each domain then compare the results.
>
> I see what you mean. Still, I wonder if it's not worthwhile if only because it expresses two bound constraints as 1 and therefore reduces the number of Lagrange multipliers that fmincon has to deal with. Then again, if that were true, I guess no one would ever use bound constraints...

As Bruno says, this is a POOR solution.

Suppose that fmincon starts in one of these
disjoint sets? It can essentially never escape
to the other piece if that is necessary.

Merely because this "reduces" the complexity
of the problem by having fewer constraints is
not a useful gain here.

Solve the problem as two disjoint problems,
then take the better solution of the two.

John
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