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Re: Overdetermined Matrix Equation Subject to Constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg122378] Re: Overdetermined Matrix Equation Subject to Constraints
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 27 Oct 2011 06:28:34 -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}, unknown]

{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>