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Overdetermined Matrix Equation Subject to Constraints


Hi all,

I have an overdetermined matrix equation that I have been solving with
LeastSquares[].  However, LeastSquares[] gives me solutions that don't
fit my constraints (that all components of x >= 0).
I know that Minimize[] and NMinimize[] minimize equations subject to
constraints, but I cannot determine if they will minimize a *matrix*
equation.
Any ideas?

Here is some sample code:

referenceData = {{1.022299535`, 1.01884186`}, {0.15627907`,
    0.716793488`}, {0.014162791`, 0.087627628`}};
testData = {0.546942055`, -0.126062557`, -0.338173002`};
Print["LeastSquares soln: ", LeastSquares[referenceData, testData]];

unknown = {x, y};
Print["Minimize soln: ",
  Minimize[{referenceData.unknown - testData,
    unknown[[1]] >= 0 && unknown[[2]] >= 0}, unknown]];



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