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From Konstantin Berlin <kber...@gmail.com>
Subject Re: [Math] Old to new API ("MultivariateDifferentiable(Vector)Function")
Date Sat, 01 Dec 2012 23:04:57 GMT
> There are probably various way to look at a "problem".
> 
> For example, I have a leastsquares "problem" but evaluating the derivatives
> is expensive (finite differences), so I nevertheless use the classes in
> "direct" (no derivatives).
> 
> [We had another discussion (raised by someone who detected what could be
> assimilated to bugs) about the "Complex" class (cf. MATH-667). But since
> nobody actually uses this class (in ways that trigger the issues), there
> is no push to implement another "view". Not sure that illustrates a point
> somehow... :-)]
> 

I am sorry, but being somewhat familiar with the topic the view you presented seems incorrect
and opposite to how people in the field use optimizers. The reason why you have newton based
methods is because quadratic approximation pretty much beats any other approach to minimization.
The convergence rate is significantly faster than direct methods, so it more than makes up
for the fact that you have to compute derivatives. The only time you should switch to a direct
method is if your energy landscape is rough and bumpy (like in a simulation).

I refer you to slide 20 and beyond, with the link below:

http://www.cs.umd.edu/users/oleary/a607/607unc2hand.pdf
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