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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