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MathGroup Archive 2004

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Minimization problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50878] Minimization problem
  • From: greg.dermer at intel.com (Greg Dermer)
  • Date: Sat, 25 Sep 2004 01:55:24 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In addition to a minimization problem, I'm also having a posting
problem.  Please bear with me if you see this more than once.

I posted a similar question to this yesterday, but it looks like it
never
made it out.

I'll preface this by saying that I'm neither a Mathematica nor
optimization
expert by any means...

I have two vectors, say x and y, of equal length of a few hundred to a
few
thousand real numbers.  I want to find new vectors, x' and y' such
that a
constraint function f(x',y')=0 is satisfied and such that x' is
"close" to x
and y' is "close" to y.  The metric for closeness that I'm considering
is
norm(x'-x) and norm(y'-y), i.e. $(x',y') = norm(x'-x) + norm(y'-y).

After a little more thought, I find I can restate the problem so that
the
explicit constraint function is eliminated by solving it for y', (y' =
g(x')) and can thus be implicitly applied through the cost function
$(x') =
norm(x'-x) + norm(g(x')-y)

It seems like I should  be able to use NMinimize to do this, but after
brief
study, inspiration has yet to strike.  I'm also not sure NMinimize is
the
right tool for data sets in the hundreds or thousands, since I've
never used
it before.

Any suggestions?

-- Greg


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