Re: optimization
- From: spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter Spellucci)
- Date: Tue, 14 Mar 2006 11:01:04 +0000 (UTC)
In article <1142329904.374048.142870@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
chrismgp@xxxxxxxxx writes:
Dear all,depends on the class of functions you want to consider:
I have a question about heuristics that I hope someone could help me
with.
Imagine a general heuristic problem. In general, as one increases the
number of variables that need to be optimized, the number of local
optima in this optimization surface increases. Although this seems to
make sense intuitively, I'm looking for papers/books/people addressing
this issue. In particular, I'd like to know if this increase in the
number of local optima is a general phenomenon in optimization
problems.
I'd appreciate any input you might have.
Please send responses to my email: jas2339@xxxxxxxxx
Thanks a lot!
Jason
a uniformly convex function on a nonempty convex set has exactly one
minimizer whatever the dimension of the space might be. but if you have a
problem with some given properties and now append a new variable say x(n+1)
and simply add the term sin(x(n+1))^2 to the objective function, you get
countably many copies of the original stationary points for the new problem
(with component k*pi k in the integers appended in the (n+1)-th component)
hence your question makes little sense in this generality
hth
peter
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