Re: LeastSquares using LinearProgramming?
- To: mathgroup at smc.vnet.net
- Subject: [mg89032] Re: [mg88986] LeastSquares using LinearProgramming?
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Sat, 24 May 2008 03:53:28 -0400 (EDT)
- References: <200805230705.DAA25655@smc.vnet.net>
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
That objective function would be quadratic, so no, LinearProgramming
will not like that.
You could instead try
FindMinimum[{objective,constraints}, vars,
Method->"QuadraticProgramming"]
This method is, alas, not documented, and I'd imagine it could disappear
(which would be a shame, because it works really well, bordering on
magic, for some problems). A documented alternative that might work well
is "InteriorPoint";, as it also can handle e.g. nonnegativity constraints.
If you can settle for an L_1 norm (so it's no longer least squares), you
can minimize a new variable abs, with new constraints -abs<=m.x-b<=abs.
Daniel Lichtblau
Wolfram Research
- References:
- LeastSquares using LinearProgramming?
- From: Gareth Russell <russell@njit.edu>
- LeastSquares using LinearProgramming?