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Minimization problem

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

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
made it out.

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

I have two vectors, say x and y, of equal length of a few hundred to a
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
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
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
study, inspiration has yet to strike.  I'm also not sure NMinimize is
right tool for data sets in the hundreds or thousands, since I've
never used
it before.

Any suggestions?

-- Greg

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