       FindMinimum within a specific interval

• To: mathgroup at smc.vnet.net
• Subject: [mg32600] FindMinimum within a specific interval
• From: "Wassim T. Jalbout" <wj01 at aub.edu.lb>
• Date: Thu, 31 Jan 2002 01:45:23 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear all,

I have the following 3 simultaneous equations

eq1      x + y + z - 1=0
eq2      -65.96x - 55.87y + 132.19z=0
eq3      174.23x + 148.29y - 380.11z=0

and I want to find the triplet (x,y,z) that best satisfies them within the
interval 0>x>1,
0>y>1 and 0>z>1.

I realize, by using Solve, that the exact solution to simultaneous eqs 1 to
3 above, namely
(x=-3.6,y=4.5,z=0.1), lies outside the [0,1] interval for x and y and is
thus uninteresting to my work.

So I thought of minimizing the following expression:
eq1^2+eq2^2+eq3^2
within the interval 0 to 1 for (x,y,z)

to do so I used FindMinimum as follows:

FindMinimum [ (x + y + z - 1)^2 + (-65.96x - 55.87y + 132.19z)^2 +

(174.23x + 148.29y - 380.11z)^2, {x, 0.1}, {y, 0.6},

{z,0.3}]

where I can only specify starting points rather than fixed intervals for x,
y and z.(unfortunately).

The result I get is:
{1.0107607*^-28, {x->-3.6, y->4.5, z->0.10}}
with x,y,z values still outside the 0,1 interval.

How to to find the x,y,z value between 0 and 1 that results in the smallest
value to my second degree expression written above? Is my approach wrong
alltogether?

I would appreciate any help,
Wassim.

--------
Wassim Jalbout, MS, D.ABMP, D.ABR
American University of Beirut,
Medical Center
Bliss St/ P.O.Box 113-6044
Beirut - Lebanon
Tel- 961 3 654255/ 961 1 344839/ 961 1 374444 ext.5090
Fax- 961 1 370795/ 961 1 345325

```

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