Re: Overdetermined Matrix Equation Subject to Constraints

*To*: mathgroup at smc.vnet.net*Subject*: [mg122382] Re: Overdetermined Matrix Equation Subject to Constraints*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Thu, 27 Oct 2011 06:29:18 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201110262138.RAA00035@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

Minimize[{referenceData.{x, y} - testData // Norm, x >= 0 && y >= 0}, {x, y}] {0.402716, {x -> 0.499807, y -> 5.8375*10^-10}} Bobby On Wed, 26 Oct 2011 16:38:36 -0500, Meaghan <freecaptive6914 at gmail.com> wrote: > 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]]; > -- DrMajorBob at yahoo.com

**References**:**Overdetermined Matrix Equation Subject to Constraints***From:*Meaghan <freecaptive6914@gmail.com>