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:
> 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
That objective function would be quadratic, so no, LinearProgramming
will not like that.
You could instead try
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.
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