Re: AE solver with bounded values for variables.

beliavsky_at_aol.com
Date: 03/18/05 

Date: 18 Mar 2005 10:06:08 -0800

kheder wrote:
> Hi,
>
> I'm using the nleq2 code to solve a system G(Y) =0 of algebraic
equations
> (see http://www.zib.de/Numerik/numsoft/CodeLib/codes/nleq2/) . The
G(Y) = 0
> is resulting from the modelling of a distillation column. Thus some
> components Y(i) represents molar fraction variables (MFV) in the
column and
> their values must be always in [0, 1]. When a MFV is negative the
program
> will stop because some procedures (bubble and dew temperatures .)
will face
> illogical operations (like division by zero) or divergence.
>
> The problem I face is in the way that nleq2 changing the Y(i) values
during
> its iterations. All guess values which I use to initiate the
resolution are
> good (MFV are inside [0, 1]), but when nleq2 begins its iterations,
it
> starts to change some MFV into negative values and then the
resolution is
> stopped.

> My problem could be solved if I could find an algebraic equations
(non
> linear) solver witch accepts to consider some variables to vary
inside
> defined boundaries.

> PS.
>
> I have to use a numerical Jacobian matrix.

If you formulate the problem as a nonlinear optimization, trying to
minimize the sums of the squared deviations of (LHS - RHS) for each
equation, you can use one of the bound-constrained optimization
programs at
http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Categories/boundconopt.html
or http://users.bigpond.net.au/amiller/ (search "bound").
Alternatively, you could use an unconstrained optimization routine and
a penalty function to keep the solution within bounds, or transform
variables of the objective function using a logistic so that the
effective parameters are forced to be within the desired bounds. I
think its best to use a constrained optimization code.

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