[SciPy-User] scipy optimization: inequality constraint type

[Kirill Balunov]

I'm sorry, I understand that's because the only solver for constrained
optimization in scipy is *SLSQP*?

But, It is not good idea to write about a particular case as if it is a
general ->

In documentation -> "In general, the optimization problems are of the form:
..."
https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.minimize.html

Which is not true in general :)


-gdg

2017-05-26 14:18 GMT+03:00 Kirill Balunov <kirillbalunov at gmail.com>:

> David, KKT conditions are first-order necessary conditions which are
> applicable if some assumptions are satisfied (regularity, continuity,..).
> The points which satisfy KKT are said to be stationary (or candidate)
> points (min, max or inflation). Internally this conditions use gradient of
> Lagrange function -> c^T * x + lambda^T * h(x) + mu^T * g(x) (this is
> classical notation), where h(x) are equality and g(x) are inequality (g(x)
> <= 0) constraints respectively. Also there is a restriction among others
> for `mu` to be non-negative. This is classical formulation of NLP (which
> looks for minimum). Of course mathematics is simply a human game with some
> rules. So you can choose from four cases (for "inequality term"):
> 1) +  mu^T * g(x),  mu >= 0,  g(x) <=0   (classical)
> 2) -  mu^T * g(x), mu >= 0, g(x) >= 0
> 3) + mu^T * g(x),  mu <= 0,  g(x) >= 0    ( awkward)
> 4) - mu^T * g(x),  mu => 0,  g(x) <= 0    (awkward)
>
> Tрe last two are awkward they roughly crash the dual problem principle
> (the related maximization problem but in Lagrange multipliers). The first
> two look good but the  the second one is very unusual. That is why I ask
> about historical reasons, why this form was chosen?
>
> -gdg
>
>
>
> 2017-05-26 1:03 GMT+03:00 David Goldsmith <eulergaussriemann at gmail.com>:
>
>> The KKT reference exceeds my numeracy...
>>
>> Anyway, i doubt this is the case, but if it's really a problem, you can
>> always write wrappers to automate the desired transformations, yes?
>>
>> DLG
>>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/scipy-user/attachments/20170526/8d4074a3/attachment.html>