# [Numpy-discussion] [SciPy-User] [ANN] Guaranteed solution of nonlinear equation(s)

Dmitrey tmp50 at ukr.net
Wed May 25 03:28:56 EDT 2011

```   --- Исходное сообщение ---
От кого: "Yosef Meller" <yosefmel at post.tau.ac.il>
Кому: scipy-user at scipy.org
Дата: 25 мая 2011, 08:54:16
Тема: Re: [SciPy-User] [ANN] Guaranteed solution of nonlinear
equation(s)

On ??? ????? 24 ??? 2011 13:22:47 Dmitrey wrote:
>  Hi all,
>    I have made my free solver interalg (     http://openopt.org/interalg     ) be
>    capable of solving nonlinear equations and systems of them. Unlike
>    scipy optimize fsolve it doesn't matter which functions are involved -
>    convex, nonconvex, multiextremum etc. Even some discontinuous funcs
>    can be handled. If no solution exists, interalg determines it rather
>    quickly.
>
Interesting. Is there any description of the actual algorithm? I tried looking
for it in the link and the openopt site, but couldn't find it.

Algorithm belongs to family of interval methods. Those ones, along
with Lipschitz methods, are capable of doing the task (searching
extremum with guaranteed precision), but require extremely much
computational time and memory, thus are very rarely used. Some ideas
created and programmed by me increased speed in many orders (see that
benchmark vs Direct, intsolver and commercial BARON), memory
consumption also isn't very huge.
As for solving equations system, currently |f1| + |f2| + |f3| + ... +
|f_k| is minimized (| . | means abs( . )). I know better way of
handling nonlinear systems by interalg, but it would take much time to
write those enhancements (maybe some weeks or even more), my current
work doesn't allow me to spend so much time for interalg and other
openopt items development.
Regards, D.
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