Re: LeastSquares using LinearProgramming?

• To: mathgroup at smc.vnet.net
• Subject: [mg89054] Re: LeastSquares using LinearProgramming?
• From: Christopher Henrich <chenrich at monmouth.com>
• Date: Sat, 24 May 2008 03:57:32 -0400 (EDT)
• References: <g15ql7\$pb3\$1@smc.vnet.net>

```In article <g15ql7\$pb3\$1 at smc.vnet.net>,
Gareth Russell <russell at njit.edu> 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

I think what you want is called "quadratic programming." It is like
linear programming in that you are looking for a point whose coordinates
satisfy linear inequalities ( and equalities), but you want to minimize
a quadratic function rather than a linear one.

I recently looked for references on linear and quadratic programming.
There are shelves of books on linear programming, but much less on
quadratic programming.  Among the books that I consulted, the most
helpful was /Linear/ /Programming/ /and/ /Extensions/ , by George
Dantzig. An oldie but a goodie.

--
Christopher J. Henrich
chenrich at monmouth.com
htp://www.mathinteract.com

```

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