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Alfonso

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11 Mar 2013 fminsearchbnd, fminsearchcon Bound constrained optimization using fminsearch Author: John D'Errico

Hi again,

thanks for your "non-answer".

My previous comment was just a general question on box constrained optimization using variable transformation, and not a critics on your code (which, btw, I judge 4 stars).

Thought it is just a wrapper..., I have not doubts on the quality of your work....

However, in a real world, multidimensional problems are very common and they need to be solved without waiting years to converge to the minimum.

In this context, gradient-based methods (e.g. L-BFGS, SD or CG) can be used togheter with variable transformation.

Then, I ask you again, how can we avoid to be stuck on the bonduary of the constraints (where the transformation gradient is 0)?

This is not a trivial problem, and it can lead to early stopping the optimization iterations on a sub-optimal saddle point.

Regards, Alfonso

24 Aug 2012 fminsearchbnd, fminsearchcon Bound constrained optimization using fminsearch Author: John D'Errico

Hi John,

One simple question for you.

When you apply a quadratic transformation x=y^2 for x>=0 (btw, the same question holds for sin(x)); how you prevent the case that the optimizer is stuck on the bonduary (y=0)? Indeed, in the case that the actual solution is not on the bonduary, but during optimization iterations your gradient-based optimizer arrives in a point that lies on the bonduary, it cannot improve towards the minimum since the transformation gradient is 0 (dx/dy=2y=0) there.

I hope I was clear enough,

thanks in advance for your kind answer.

Alfonso

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