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Subject: Re: Optmizaing a vector of 1-D functions
Date: Thu, 8 Apr 2010 19:47:07 +0000 (UTC)
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James Allison <james.allison@mathworks.com> wrote in message <hplaai$9l$1@fred.mathworks.com>...
> They are independent in the sense that it is possible to evaluate each 
> function independently, but the functions are coupled through the shared 
> optimization variable x. If Andrey is seeking a single optimal value of 
> x for the whole set of objective functions, the tradeoffs between the 
> objective functions will need to be considered. A value of x that is 
> best for one function may not be best for another. See my notes about 
> multi-objective optimization.
> 
> -James
---------
  That's not my understanding of Andrey's statement, James.  In his second article in this thread he wrote: "I mean, I've got a vector-function of one variable: F(x) = (f1(x), ..., fn(x))' where x is a real number. My problem is that I need to attain (x1, ..., xn)' where xj is a maximum of fj(x) over some interval (a,b)."

  In other words he is *not* "seeking a single optimal value of x for the whole set of objective functions", if we are to accept his statement in the second article.  Each of the n optimal values of x is to maximize the corresponding f in his vector of functions.

Roger Stafford