Optimisation mit constraint

• To: mathgroup at yoda.physics.unc.edu
• Subject: Optimisation mit constraint
• From: Colin Rose <colinr at extro.ucc.su.oz.au>
• Date: Tue, 24 Nov 92 3:55:21 EST

```   Rod Price writes:
>> I need to minimize a function of about thirty variables subject to
>> three constraint equations, each of which involves all thirty
>> variables.  If I didn't have the constraints, I would use something
>> like FindMinimum[] to do the minimization numerically. On the other
>> hand, if I had only a few variables, I would use Lagrange multipliers
>> to solve the minimization problem by hand.  Unfortunately, I can't do
>> either, so:  Is there a way of minimizing my function numerically in
>> Mma with the constraints?

If your function is linear (and if your constraints are linear), you can
use ConstrainedMin[]. If it is NOT linear, may I suggest:
1.  Specify the Lagrangean in Mma: call it L. Then...
2.  NSolve[ { D[L, x1]      == 0,
D[L, x2]      == 0,       etc
D[L, lambda1] == 0,       etc   },
{x1, x2, ..., x30, lambda1, lambda2, lambda3} ]

which may do it for you. Of course, if you have 30 variables, this
may prove somewhat tedious. If my memory serves me correctly,  Hal Varian
has a package that automates much of the tedium in this respect in his
book...

Varian, Hal (1992), Economic and Finanical Modeling with Mma....

It should be out before the year's end.

Regards

Colin

Colin Rose
Dept. of Economics
University of Sydney
colinr at extro.ucc.su.oz.au
*************************

```

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