🚀 go-pugleaf

> I have the following problem, and not being familiar with 
> minimization techniques, am appealing to net gurus for help
> 
> I need to solve the linear system 
> 
>               A x = b
> 
> where A is an NxN matrix 
>       x is a N vector,
>   and b another N vector,
> 
> subject to the constraint that each of the x_i , i=1,..,N are
> positive.
> 
> The  thing to do seems to be to minimize 
> 
> || Ax -b|| subject to  x_i > 0.
> 
> 
> Now the question is how. I cannot formulate the above inequality as an
> over-det system for example and use some standard SVD code. 

One method I've used is called Hildreth's method.  The reference is
Luenberger, "Optimization by Vector Space Methods," Wiley, 1968,
pages 299-300.  It's a pretty straight-forward iterative method.
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Dan Simon