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constrained minimization -- Minimize/Reduce don't work

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  • Subject: [mg48576] constrained minimization -- Minimize/Reduce don't work
  • From: Sharath <csr at>
  • Date: Sat, 5 Jun 2004 07:19:36 -0400 (EDT)
  • Organization: Washington University in St. Louis
  • Sender: owner-wri-mathgroup at


Using Mathematica 5.0 I am trying to minimize a non-linear function (for 
f(w,u,v,x,y,z) = (w(wx-y)Log(xu)v+3(Log(x)+w(1-z)Log(1/y))) 

with some constraints like {w,u} are postive Integers {v,x,y,z} are 
Reals with v>=0, x>1, 0<y<1, 0<z<1.

I tried using  Minimize[{f, cons}, {x, y,...}] but it gives 
"Minimize::mixdom: Exact optimization with mixed real and integer 
variables is not yet implemented".

So I removed the restriction of Integers but then it gives me the entire 
expression as it is!

I tried using Reduce by using f>0 as the expression. When used with or 
without ForAll quantifier for variables either I get
"Reduce::nsmet: This system cannot be solved with the methods available 
to Reduce" (even though I tried simplifying the expression and 
eliminating some of the varibles some values).

I thought this constrained minimization can be solved using Lagrange 
multipliers method (do I need to change < to <=?).
Ideally, I would like x and y expressed in terms of z. Is it possible to 
  do such a thing -- get symbolic values for x and y to minimize f?

Which function can I use or do I need to put the Lagrange Multiplier 
equations myself and try solving.
This is my first use of Mathematica. I went through various examples to 
learn the basics.

Any help is appreciated. Thanks.


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