Hi !
I am trying to express a quadratic function in the form
1/2 x’ Q x + a’ x in GAMS ( ’ means the transpose) because I would like to generate random PSD Q matrices with MATLAB and export to GAMS with *.gdx files.
I think that with the following example it will more clear what i need:
If we consider the following quadratic function given by f(x) = 1/2 x’ * Q * x + a’ * x
with a’ = [ 1 1] and Q = [2 1; 1 2]
I can expand the quadratic function and type in GAMS as
f(x) = x1^2 + x2^2 + x1*x2 + x1 * x2
However I need to express the quadratic equation in function of Q and a.
I tested to do somthing similar that when I need to multiply 3 matrices in gams:
t’ * Q * t
where
t’ = [ 1 1] and
Q = [2 1; 1 2]
\
Set
n /n1*n2/
;
Alias (n, k)
;
Parameters
tT(i) / n1 1, n2 1/
C(i)
H
;
Table Q(n,n)
n1 n2
n1 2 1
n2 1 2
;
C(n) = sum(k, aT(k) * B(n,k ) ) ;
H = sum(k, C(k) * aT(k));
display H
;
But does not work.
Thank you for your time,
Juan
\
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