symbolic constrained minimization -- Minimize/Reduce don't work

• To: mathgroup at smc.vnet.net
• Subject: [mg48577] symbolic constrained minimization -- Minimize/Reduce don't work
• From: csr at postmark.net (Sharath)
• Date: Sat, 5 Jun 2004 07:19:40 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

Using Mathematica 5.0 I am trying to minimize a non-linear function
(for example),
f(w,u,v,x,y,z) = (w(wx-y)Log(xu)v+3(Log(x)+w(1-z)Log(1/y)))/(1-y)Log(x)-w^2(x-1)(z-1)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.

-Sharath

```

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