       Solving non-linear equations

• To: mathgroup at smc.vnet.net
• Subject: [mg5468] Solving non-linear equations
• From: elisha at dot.net.au (Luci Ellis)
• Date: Sat, 7 Dec 1996 00:26:50 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```Hello Mathgroup.

One of my colleagues and I are trying to solve out first-order conditions
from an optimisation problem. I had written a neat little function that
does all the necessary transformations. We can get the first order
conditions really easily, but they seems to eat up so much RAM that it just
refuses to solve -- instead the kernel quits.

Here is a simplified version of the problem. Even it doesn't work and we
REALLY want to do a more complex version.

It's okay if there are multiple solutions, we are expecting that. We want
to solve it out analytically to ensure that we have global minima, so

Anyway, we want to solve this problem

focs = {0.0175051*a1^2*a2*a3 + 0.25669*a1*a2*a3*d1 - 193.*d2*d3 +

0.0175051*a1*d1*d2*d3 + 0.25669*d1^2*d2*d3 == 0,

-193.*a2*a3 + 0.0145715*a1^2*a2*a3 + 0.0175051*a1*a2*a3*d1 +

0.0145715*a1*d1*d2*d3 + 0.0175051*d1^2*d2*d3 == 0,

-0.26055*a1*a2^2*a3 + 0.0145715*a1*a2*a3*d2 - 193.*d1*d3 -

0.26055*a2*d1*d2*d3 + 0.0145715*d1*d2^2*d3 == 0,

-193.*a1*a3 + 33.6978*a1*a2^2*a3 - 0.26055*a1*a2*a3*d2 +

33.6978*a2*d1*d2*d3 - 0.26055*d1*d2^2*d3 == 0,

-193.*a1*a2 + 0.25669*a1*a2*a3^2 - 0.42074*a1*a2*a3*d3 +

0.25669*a3*d1*d2*d3 - 0.42074*d1*d2*d3^2 == 0,

-0.42074*a1*a2*a3^2 - 193.*d1*d2 + 33.6978*a1*a2*a3*d3 -

0.42074*a3*d1*d2*d3 + 33.6978*d1*d2*d3^2 == 0}

with respect to the algebraic objects: vars = {d1, a1, d2, a2, a3, d3}

And thus get replacement rules {d1 -> some real number, d2 -> another real
number... and so on.

Does anyone know why Solve[focs,vars] eats so much RAM?

Please email me at elisha at dot.net.au

Thanks in anticipation.

Luci Ellis

```

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