using optimize() correctly ...

Yes.  Most classical optimization methods (e.g. gradient-type, Newton-type) are "local", i.e. they do not attempt to locate the global optimum.  The primary difficulty with global optimization is that there are no mathematical conditions that characterize global optimum in multi-modal problems.  For local optimum, you have the first- and second-order Kuhn-Tucker conditions.  A simplistic strategy to find global optimum is to use local methods with multiple starting values.  Again the problem is that you don't haev any guarantee that you have found the global optimum.  The larger the number of starting values, the greater your chances of finding the global optimum.  There are more principled strategies than the random multi-start approach, but even they are not guaranteed to work.  

Ravi.

____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: Esmail <esmail.js at gmail.com>
Date: Sunday, May 24, 2009 8:27 am
Subject: Re: [R] using optimize() correctly ...
To: Berend Hasselman <bhh at xs4all.nl>
Cc: r-help at r-project.org

Hello Berend,
 
 Berend Hasselman wrote:

 > 
 > 
 > Your function is not unimodal.
 > The help for optimize states: 
 > 
 > "If f is not unimodal, then optimize() may approximate a local, but 

perhaps

 > non-global, minimum to the same accuracy."

 
 Ah ok, I didn't read the manual page carefully enough.
 
 Do you know if R has a function to find the global maximum/minimum of 
a
 function of x over a given interval?
 
 nlminb(), optim(), in particular the option `method = "L-BFGS-B"' or 
the 
 function spg() in "BB" package were recommended to use if I wanted to
 optimize a function over x and y given their respective intervals. Will
 they also potentially only give me the local maxima/minima? I am not 
a
 regular R user, so my knowledge is clearly not where is could/should 
be.
 
 Thanks,
 Esmail
 

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