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 Radiation Physicist Radiation Oncology Department 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