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