Recommendations for a large scale bounded variable least squares (BVLS) solver for sparse matrices - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T11:57:30Z http://mathoverflow.net/feeds/question/27713 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/27713/recommendations-for-a-large-scale-bounded-variable-least-squares-bvls-solver-fo Recommendations for a large scale bounded variable least squares (BVLS) solver for sparse matrices Jacob 2010-06-10T15:59:16Z 2010-08-12T21:08:51Z <p>I'm trying to solve the BVLS problem for huge (2e6x2e6) matrices which are very sparse (4 elements per row). Does anybody have a recommendation for a free solver (preferably a library of routines)?</p> <p>The BVLS problem is defined as:</p> <p>\$\underset{l \le x \le u}{\min} \lVert Ax - b \rVert_2^2\$</p> http://mathoverflow.net/questions/27713/recommendations-for-a-large-scale-bounded-variable-least-squares-bvls-solver-fo/27902#27902 Answer by alext87 for Recommendations for a large scale bounded variable least squares (BVLS) solver for sparse matrices alext87 2010-06-12T05:31:05Z 2010-06-12T06:06:09Z <p>This is such a well-solved problem that there are many software packages that have built in functions for this. </p> <p>Here are a selection of built-in functions in different software packages that can be used: </p> <p>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.)</p> <p>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. </p> <p>For a free solver I have found this: <a href="http://sourceforge.net/projects/quadprog/" rel="nofollow">http://sourceforge.net/projects/quadprog/</a> 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.</p>