This is such a well-solved problem that there are many software packages that have built in functions for this.
Here are a selection of built-in functions in different software packages that can be used:
In Matlab: lsqlin (type help lsqlin into Matlab and it tells you exactly what to type. I have just (approximately) solved your problem with random sparse matrices and it works great.)
KNITRO for Mathematica this package also solves this exact problem but I don't have this software so I can't tell you which exact function.
For a free solver I have found this: http://sourceforge.net/projects/quadprog/
However it assumes that $A$ has full column rank. This is just because this algorithm uses the dual problem which exists when the Hessian $A^TA$ is positive definite.
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