|11 Mar 2013||fminsearchbnd, fminsearchcon Bound constrained optimization using fminsearch||Alfonso||
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.
|24 Aug 2012||fminsearchbnd, fminsearchcon Bound constrained optimization using fminsearch||Alfonso||
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.