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Subject: Re: [Math] Old to new API
 ("MultivariateDifferentiable(Vector)Function")
From: Konstantin Berlin <kberlin@gmail.com>
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Date: Sat, 1 Dec 2012 18:04:57 -0500
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To: "Commons Developers List" <dev@commons.apache.org>

> There are probably various way to look at a "problem".
>=20
> 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).
>=20
> [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... :-)]
>=20

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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