FindMinimum and picewise linear functions

• Subject: [mg2679] FindMinimum and picewise linear functions
• From: sinan at u.washington.edu (Sinan Karasu)
• Date: Tue, 5 Dec 1995 02:26:41 -0500
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: University of Washington, Seattle

```
I define a piecewise linear function with If statements,
and then sample the function on a list. And then I try
to do an optimization on it (sum of squares...)
FindMinimum always complains about not being able
to find the gradient. Has anyone come up with a way
to do this?

Let us say I define (0,1)->R^2 to be a triangle
Then I sample it on say {0.1,0.3,0.5,0.7,0.9} and then
I come up with another sampling, say {0.1,0.3,0.4,0.7,0.9}

Now if I do Sum[(triangle1samples[[i]]-triangle2samples[[i]])^2,{i,1,5}]
and then perturb {0.1,0.3,0.t+4,0.7,0.9} and do a minimization
of Sum over the second sample (i.e. t) FindMinimum complains
about not being able to take the gradient. I unserdtand why
it does, the question is, can I circumvent this somehow????

Sinan

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```

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