Alessandro
06-16-2009, 11:34 AM
Hi all,
I have a constrained minimization problem for which I wonder if a
closed form solution, i.e., no numerical algorithm, exists.
I have a vector x of 5 unknowns, such that
PHI * x = 0
where PHI is a matrix with 4 rows, but in general, because of noise problems, more rows should be considered.
Moreover, rank(PHI)=4 or, because of noise rank(PHI) =5, with the smaller singular value close to zero.
In addition, the following constrain arises (on
the first 2 components):
x_1^2 + x_2^2 = 1
that takes into account that, actually, x_1=cos(alpha) and x_2=sin(alpha).
Is there an analytical and elegant solution for that?
Thanks,
Alessandro
I have a constrained minimization problem for which I wonder if a
closed form solution, i.e., no numerical algorithm, exists.
I have a vector x of 5 unknowns, such that
PHI * x = 0
where PHI is a matrix with 4 rows, but in general, because of noise problems, more rows should be considered.
Moreover, rank(PHI)=4 or, because of noise rank(PHI) =5, with the smaller singular value close to zero.
In addition, the following constrain arises (on
the first 2 components):
x_1^2 + x_2^2 = 1
that takes into account that, actually, x_1=cos(alpha) and x_2=sin(alpha).
Is there an analytical and elegant solution for that?
Thanks,
Alessandro