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Topic: Preventing negative values in fmincon
Replies: 10   Last Post: May 28, 2008 12:03 PM

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Nicolas

Posts: 16
Registered: 4/9/08
Re: Preventing negative values in fmincon
Posted: May 23, 2008 12:30 PM
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"John D'Errico" <woodchips@rochester.rr.com> wrote in
message <g16p8v$5ee$1@fred.mathworks.com>...
> "Mike " <michael.gerstREMOVE@yale.edu> wrote in message
> <g16n7a$9m8$1@fred.mathworks.com>...

> > Bruno and John, thanks for the tip.
> >
> > If I understand you correctly, the following simple LP

problem
> >
> > Obj = a*X1 + a*X2 + a*X3
> > subject to: X1 + X2 + X3 =< b
> >
> > would transform to
> >
> > Obj = a*sqrt(X1^2) + b*sqrt(X2^2) + c*sqrt(X3^2)
> > subject to: sqrt(X1^2) + sqrt(X2^2) + sqrt(X3^2) =< b
> >
> > Is this the basic idea?

>
> Not exactly. Have the optimizer vary a vecotr
> with three unknowns in it [Y1,Y2,Y3]. Inside
> the objective function, transform your
> variables so that
>
> X1 = Y1^2
> X2 = Y2^2
> X3 = Y3^2
>
> So now X1, X2, X3 are assured to be positive.
>
> When the optimization is done, and it returns
> the vector [Y1, Y2, Y3], just square the elements
> to recover [X1, X2, X3].
>
> There are similar strategies to deal with variables
> that have both upper and lower bounds.
>
> John


If these strategies are not adapted to the problem, you may
also try knitro through the ktrlink function of the
toolbox. Indeed, knitro has a "feasible" mode that
guarantees that it stays in the feasible domain once it has
found a feasible solution.

I can provide you with a one-month test licence if needed.
Just send an email to support-knitro@artelys.com.

Nicolas.



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