[CppAD] Using existing derivative code combined with AD

[Piotr Dobaczewski]

Hi Brad, hi Marcel

Thank you for your answers, they've answered my question, however I 
probably won't decide to use CppAD in my case. Maybe I should have 
elaborated more: I was hoping to solve problems with such "g-s" using 
Ipopt solver via the high level OS (Optimization Services of COIN-OR) 
interface. As far as I see this requires the problem to be processed by 
AD (or am I missing something?).

User atomic would seem like the way to go, but I think I will rather 
revert to using Ipopt through its "bare" interface.

Pozdrawiam
Piotr Dobaczewski

W dniu 2013-03-16 14:12, Brad Bell pisze:
> On 03/15/2013 03:24 AM, Marcel Rehberg wrote:
>> Hi Piotr,
>>
>> maybe you are looking for
>>
>> http://www.coin-or.org/CppAD/Doc/user_atomic.htm
>
> 1. Note that, if your browser supports MathML,
> http://www.coin-or.org/CppAD/Doc/user_atomic.xml
> is easier to read.
>
> 2. This feature is intended to increase the speed of derivative
> evaluation for functions where you know a program that will compute the
> derivatives. You could apply this idea to the case below, but there is
> another possible alternative; see below:
>
> ... snip ...
>>>
>>> > Am Mittwoch, den 05.01.2011, 14:53 +1100 schrieb Scott Foster:
>>> >> Hi,
>>> >>
>>> >> I have a function of the form f(g(x),x,y), which has a scalar
>>> outcome.
>>> >> The function g(x) requires iteration and can't be auto-differentiated
>>> >> easily but its derivative can be found using other methods
>>> (numerical).
>>> >> The function f(.,.,.) is pretty horrible in itself but it is a
>>> >> predefined sequence of operations and is an ideal candidate for AD.
>
> There are some special tricks for AD of functions (like g) that require
> iteration to evaluate. For example, suppose that g(x) is defined by
> h(g, x) = 0
> and one uses Newton's method to iterate and solve for g(x). Then one can
> evaluate the derivative of g(x) using the formula
> h_g ( g(x) , x ) * g'(x) + h_x ( g(x), x) = 0
> where h_g is the partial of h w.r.t g and h_x is the partial of h w.r.t
> x; i.e.,
> g'(x) = - h_g( g(x), x)^{-1} h_x ( g(x), x)
>
> You could then use AD to compute h_g, and h_x. Then get g'(x), then use
> AD to get f_g, f_x, f_y, and use the chain rule to get derivatives of f(
> g(x) , x , y ). While this applies to scalar value g(x), it also applies
> to vector valued g(x) (so long as the implicit function theorem applies).
>
>
>
>
>
>>> >>
>>> >> So, what I want to do is to use AD to differentiate f(.,.,.) but
>>> to tell
>>> >> CppAD, somehow, to use the hard-wired code whenever it comes across
>>> >> g(x). I do not know how to do this. It is what I want to learn how
>>> to do.
>>> >>
>>> >> I'm assuming that this is a pretty common problem but I haven't been
>>> >> able to find any mention in the documentation. Of course, that
>>> doesn't
>>> >> mean that it isn't there -- just that I haven't found it:-)
>>> >>
>>> >> Any help would be very appreciated.
>>> >>
>>> >> Scott
>>> >>
>>> >
>>> > _______________________________________________
>>> > CppAD mailing list
>>> > CppAD at list.coin-or.org
>>> > http://list.coin-or.org/mailman/listinfo/cppad
>>> >
>>>
>>
>>
>
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