From: Matt J on
James Allison <james.allison(a)mathworks.com> wrote in message <hplaai$9l$1(a)fred.mathworks.com>...

> 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.

True, but he stated that he is not looking for a single optimal value of x.
From: Roger Stafford on
James Allison <james.allison(a)mathworks.com> wrote in message <hplaai$9l$1(a)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