squared norm in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg85764] squared norm in Mathematica
• From: syed qasim Ali <edu_forme at yahoo.com>
• Date: Thu, 21 Feb 2008 18:02:29 -0500 (EST)

```  Dear Sir,
My problem was  actually

||SX||^2
i was trying it as multiobjective optimiztaion in Mathematica but i got to know that it can be programmed as single objective ....

||SX||^2=(a11*x1 + a12*x2 + a13*x3)^2 + (a21*x1 + a22*x2 +
a23*x3)^2 + (a31*x1 + a32*x2 + a33*x3)^2.

therefore my problem becomes

x1 >= 0.52, <= 1.47;
x2 >= 0.52, <= 1.47;
x3 >= 0.52, <= 1.47;
x4 >= 0.52, <= 1.47;

minimize : ( ((-0.22*x1)+(0.13*x2)+(-0.09*x3)+(0.07*x4))^2 +
((-0.13*x1)+(0.09*x2)+(-0.07*x3)+(0.058*x4))^2 +((-0.09*x1)+(0.07*x2)+
(-0.058*x3)+(0.049*x4))^2);

subject to:
-4+x1^2+x2^2+x3^2+x4^2=0;

IN Mathematica it becomes

FindMinimum[{(-0.22 g1+0.13 g2-0.09 g3+0.07 g4)2+(-0.13 x1+0.09 x2-0.07 x3+0.058 x4)2+(-0.09 x1+0.07 x2-0.058 x3+0.049 x4)2,-4+x12+x22+x32+x42=0&&0.52£x1£1.47,0.52£x2£1.47,0.52£x3£1.47,0.52£x4£1.47},{x1,x2,x3,x4}]

i have this  result when i tried this problem in Mathematica ....i guess Mathematica can handle this problem

Set::write : Tag Plus in
-4+x12+x22+x32+x42 is Protected
FindMinimum::eqineq : Constraints in {0,0.52£x1,0.52£x2,0.52£x3,0.52£x4,x1£1.47,x2£1.47,x3£1.47,x4£1.47} are not all equality or inequality constraints. With the exception of integer domain constraints for linear programming, domain constraints or constraints with Unequal (!=) are not supported.

i donot understand where the fault lies ...when i have only one objective function

thanx

```

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