On Jul 12, 2011, at 9:33 AM, Julio Rojas wrote:
As "n" grows, the number of terms of the gradient also grow by a
factor of 8, so doing a gradient based method would be out of the
question.
If I understand you correctly, you are falling prey to a common
misconception.
Actually, there is a theorem that you can always compute the gradient
of a function with effort within a constant factor of the effort to
evaluate the function once.
To do this, however, you compute the gradient in a somewhat nonobvious
manner, known as an "adjoint method" or "backwards differentiation" or
"reverse-mode differentiation". (There are even "automatic
differentiation" tools that will implement this for you automatically.)
Another difficulty with using gradient-based methods is that, the way
you have defined your function, it is not differentiable (thanks to
"if-then" and similar piecewise definitions). As mentioned in the
NLopt introduction, however, it is usually possible to reformulate the
problem in a differentiable manner by insertion of dummy variables.
See:
http://ab-initio.mit.edu/wiki/index.php/NLopt_Introduction#Equivalent_formulations_of_optimization_problems
I decided to use "NLOPT_LN_BOBYQA", thinking it wouldn't be that
hard to solve this problem. Nonetheless, I have found that the
second constraint, which limits the maximum uncertainty of the
solution, is repeatedly violated by the solver. How can I control
this problem? Or is it a limitation inherent to the solver?
How do you even impose these constraints in BOBYQA? BOBYQA only
supports simple bound constraints.
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