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Re: LeastSquares using LinearProgramming?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89056] Re: LeastSquares using LinearProgramming?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 24 May 2008 03:57:54 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <g15ql7$pb3$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

you question is

"Is ||m.x-b||^2 linear."

and it is not.
Linear programming usual search the simplex build up
from the constrains and searches only the corners
of that simplex. Because for a linear problem c.x the
optimal value *must* be on the corners of the simplex of the
constrains. For a quadratic (that's why it is called "least squares")
this is not true.

Regards
   Jens




Gareth Russell wrote:
> Hi,
> 
> Is it possible to specify a least-squares minimization through the 
> LinearProgramming function? In other words, exactly the same as 
> LeastSquares, with the extra constraint that all x>=0?
> 
> Presumably it comes down to specifying the input c correctly in the 
> LinearProgramming function. But I can't see how to do that such that 
> what is being minimized is the standard least-squares function 
> ||m.x-b||^2
> 
> Thanks,
> 
> Gareth


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