A SHAZAM User asked:
Is it possible to solve a non-negative least-squares constraints problem of the form shown below in SHAZAM?
${\min_{x}\left \| B.x-a \right \|^2_2},\quad where\quad x\geq 0$
Could this be done with the NL command?
Yes, this can be done.
The simplest way is to specify the equation on the NL command like
EQ Y = a + (b*b)*X
will make the coefficient on X always positive because b*b is always zero or positive.
You could also create a SHAZAM procedure using the PROC command which for two variables might look like this:
* PROC NNLS2
*
* SHAZAM Procedure to perform Non Negative Least Squares for 2 variables
*
* INPUTS: [YIN]
* [XIN]
* [STARTIN]
*
* OUTPUTS: [BETAOUT]
*
PROC NNLS2
MATRIX X1_=[XIN](0,1)
GENR X1_=X1_
MATRIX X2_=[XIN](0,2)
GENR X2_=X2_
NL 1 / NCOEF=[VARSIN] START=[STARTIN] GENRVAR
EQ [YIN]=(B1_*B1_)*X1_+(B2_*B2_)*X2_
END
GENR B11_=B1_*B1_
GENR B22_=B2_*B2_
MATRIX [BETAOUT](1,1)=B11_
MATRIX [BETAOUT](2,1)=B22_
PROCEND
Asked: 2011-03-12 07:47:13 +0000
Seen: 228 times
Last updated: Mar 12 '11
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