Re: FindMinimum [] more elegantly?

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1575] Re: FindMinimum [] more elegantly?
• From: withoff (David Withoff)
• Date: Sat, 1 Jul 1995 02:48:06 -0400
• Organization: Wolfram Research, Inc.

```In article <3sisqj\$n9u at news0.cybernetics.net> MAMER at utkvx.utk.edu writes:
>Hello MathGroupers,
>I have a question regarding putting the FindMinimum[] into a more elegant
>form than the following which I've been using.
>I have a function sumOfSquares of two variables a and b and I need to feed
>back the values of a and b into the FindMinimum expression as follows:
>alpha= 0.234; beta= .567;
>FindMinimum[ sumOfSquares, {a,alpha}, {b,beta}, MaxIterations->100 ]
>alpha= a/.%[[2,1]] ; beta=b/. %[[2,2]];
>
>I used the to click on the last two statements several times til the output
>of FindMinimum stabilizes. Is there an elegant way to do this?
>
>Mike Amer
>mamer at utkvx.utk.edu

This behavior usually means that FindMinimum is searching around
in a broad minimum, so that any of the points in a large region
near the minimum will meet the stopping conditions specified in
the AccuracyGoal or PrecisionGoal options.  Iterating FindMinimum
can cause it to move from one point in that region to another,
but it will only by accident move in the direction of the minimum,
since any of the points in that region satisfy the stopping
conditions.  In some cases a better approach is to increase the
value of PrecisionGoal or AccuracyGoal.  In all cases, the most
thorough approach is to study the mathematics of the problem,
perhaps looking at a few plots, and try to understand the origin
of the problem.  FindMinimum does not do anything particularly
fancy, and is unlikely to show this sort of behavior unless
there is a problem in the underlying mathematics.

Dave Withoff
Research and Development
Wolfram Research

```

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