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minimization with constraints

• To: mathgroup at yoda.physics.unc.edu
• Subject: minimization with constraints
• From: brigham!rprice at physics.att.com
• Date: Fri, 20 Nov 92 19:58:17 EST

Hello all,

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?  I've found that simply programming the  
Lagrange multiplier approach numerically doesn't work, because the  
"minimum" of function + lagrange multipliers * constraints is really  
a saddle point, so no numerical method is going to find it.

Surely someone has figured out how to do this before.  Perhaps  
there's an Mma package out there?  (hope springs eternal...)

Thanks very much,

Rod Price
rprice at physics.att.com