[SciPy-Dev] New Tutorial on Optimize Help

[Phillip Feldman]

Providing a function for the derivative is almost always better than
finite-difference derivatives unless the cost of evaluating the derivative
function is very high.

On Mon, Sep 30, 2019 at 4:43 PM Christina Lee <chrissie.c.l at gmail.com>
wrote:

> Hi,
>
> I'm a SciPy technical writer and am currently rewriting the scipy.optimize
> tutorial, focusing on `minimize` right now.  While I've gotten a grasp of
> the "how", I still want to explain "why". Why choose one option over
> another? I could use information from those with more experience.
>
> A lot of methods are available.   Most problems can have BFGS thrown at
> them, but I want to explain something for those other cases.  Other
> situations could have features, like constraints or non-differentiability,
> that lend themselves to a specific method. But the module still has a lot
> of alternatives.  Are they there for academic purposes?  Are they the best
> for some problems? How could someone find that out?
>
> For derivatives, users can choose to provide a function or three different
> types of finite-difference schemes.
>
> When is providing a function better than finite-difference derivatives?
> For Hessians, approximations are sometimes more efficient.  How can we know
> in advance if that's true? Is that ever true for gradients?
>
> How do we choose which finite-difference scheme? `3-point` and `cs` (if it
> is the symmetric approximation I think) have higher-order accuracy, but
> `cs` uses a point not yet computed.  Is `3-point` ever not the way to go?
>
> Thanks for your expertise,
> Christina
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