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FindMinimum in specified range if gradient cannot be found symbolically


Dear MathGroupers,

Here's an answer from Wolfram Research's technical support
(specifically Alan DeGuzman) to my question:

"How can one find the minimum of a function in a specified range when
the gradient cannot be found symbolically?".

I expected FindMinimum in the form

FindMinimum[ foo[x], {x, xstart, xmin, xmax} ]

to work (where each argument is a single number) since it gives the
range to search AND contains a starting point - but it didn't.

The problem was one of syntax. Instead of passing a single value to
xstart, you must pass a list of two starting values. This will allow
you to use an minimum and maximum search range.

In[1]:= xstart = {2,3};

In[2]:= xmin = 1;

In[3]:= xmax = 6;

In[4]:= FindMinimum[-Abs[Sin[x/2]], {x,xstart,xmin,xmax} ]

Out[4]= {-1., {x -> 3.14159}}

This use of FindMinimum is not clearly documented so I thought I'd
share it with you all.  Alan tells me that a more thorough example of
FindMinimum[] should be included in the next version of the
Mathematica book.

Happy New Year



 Dr Simon Chandler
 Hewlett-Packard Ltd			Tel:   0272 228109
 Computer Peripherals Bristol		Fax:   0272 236091
 Filton Road, Stoke Gifford
 Bristol, BS12 6QZ	  		email: simonc at
 United Kingdom


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