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>