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