squared norm in Mathematica
syed qasim Ali
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
Curtis Osterhoudt
Though I can't necessarily read your FindMinimum command (it seems to
contain some non-standard characters), I think I see what the problem is.
That error message almost always crops up when you've tried to assign a value
to something which isn't allowed to be assigned to.
In other words, I suspect you have to replace the single equals sign ( = )
in "-4+x12+x22+x32+x42=0" with a double one ( == ).
I hope that helps!
C.O.
On Thursday 21 February 2008 16:02:29 syed qasim Ali wrote:
> 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=A3x1=A31.47,0.52=A3x2=A31.47,0.52=A3x3=A31.47,0.5
>2=A3x4=A31.47},{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=A3x1,0.52=A3x2,0.52=A3x3,0.52=A3x4,x1=A31.47,x2=A31.47,x3=A31.47,x4=A31.47}
> 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
-
==========================
==========================
========
Curtis Osterhoudt
cfo@remove_this.lanl.and_this.gov
PGP Key ID: 0x4DCA2A10
Please avoid sending me Word or PowerPoint attachments
See http://www.gnu.org/philosophy/no-word-attachments.html
==========================
==========================
========
Jens-Peer Kuska
Set[] written as "=" has nothing to do with Equal[]
written as "==" and FindMinimum[] need Equal[] and
*not* Set[]
Regards
Jens
syed qasim Ali wrote:
> Dear Sir,
> My problem was actually
>
> ||SX||^2
> i was trying it as multiobjective optimiztaion in Mathematica but i g=
ot 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=A3x1=A31.47,0.52=A3x2=A31.47,0.52=A3x3=A31.47,0.52=A3x4=A31.47=
},{x1,x2,x3,x4}]
>
>
> i have this result when i tried this problem in Mathematica ....i gu=
ess Mathematica can handle this problem
>
> Set::write : Tag Plus in
> -4+x12+x22+x32+x42 is Protected
> FindMinimum::eqineq : Constraints in {0,0.52=A3x1,0.52=A3x2,0.52=A3x3=
,0.52=A3x4,x1=A31.47,x2=A31.47,x3=A31.47,x4=A31.47} are not all equality =
or inequality constraints. With the exception of integer domain constrain=
ts for linear programming, domain constraints or constraints with Unequal=
(!=) are not supported.
>
> i donot understand where the fault lies ...when i have only one objec=
tive function
>
>
> thanx
>
>