Overdetermined Matrix Equation Subject to Constraints

*To*: mathgroup at smc.vnet.net*Subject*: [mg122353] Overdetermined Matrix Equation Subject to Constraints*From*: Meaghan <freecaptive6914 at gmail.com>*Date*: Wed, 26 Oct 2011 17:38:36 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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]];

**Follow-Ups**:**Re: Overdetermined Matrix Equation Subject to Constraints***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: Overdetermined Matrix Equation Subject to Constraints***From:*DrMajorBob <btreat1@austin.rr.com>