# [SciPy-User] optimization routines can not handle infinity values

Enrico Avventi eavventi@yahoo...
Wed Sep 15 04:15:20 CDT 2010

```Hi Matthieu,

thanx for the reply. as far as i know it shouldn't be a problem at all in
theory. in fact convergence theorems for newton methods and, in general,
descent method do not require the function to be defined everywhere. you
need just a function defined in an open convex set that has compact sublevel
sets - e.g f(x) = x - log(x). this is exactly my situation.
it is just a matter of slightly changing the line search method to reject
steps that would lead to an infinite value.
i will look at how it is implemented in scipy and see if it can be fixed
easily.

/Enrico

On Tue, Sep 14, 2010 at 5:51 PM, Matthieu Brucher <
matthieu.brucher@gmail.com> wrote:

> Hi,
>
> There are two categories of contraints optimizations:
> - you can evaluate the function outside the constraints
> - you cannot evaluate the function outsde the constraints.
>
> If the first one can be handled by more general algorithms providing some
> tricks, you cannot use them for the second one. Your problem is clearly a
> second category problem, so you must use appropriate algorithms (which may
> not be available in scipy directly, you may want to check OpenOpt).
>
> It's not a problem of routines, it's a problem of appropriate algorithms.
>
> Matthieu
>
> 2010/9/14 enrico avventi <eavventi@yahoo.it>
>
>> hello all,
>>
>> i am trying out some of the optimization routines for a problem of mine
>> that is on the form:
>>
>> min f(x)
>>
>> s.t M(x) is positive semidefinite
>>
>> where f is strictly convex in the feasible region with compact sublevel
>> sets, M is linear and takes value in some subspace of hermitian matrices.
>>
>> the problem is convex but the costraint can not be handled directly by any
>> of the optimization routines in scipy. So i choose to change it to an
>> uncostrained problem with objective function:
>>
>> f1(x) = f(x) for M(x) pos semi def
>> f1(x) = Inf otherwise
>>
>> the problem is that it seems the routines can not handle the infinity
>> values correctly.
>>
>> Some of the routines (fmin_cg comes to mind) wants to check the gradient
>> at points where the objective function is infinite. Clearly in such cases
>> the gradient is not defined - i.e the calculations fail - and the algorithm
>> terminates.
>>
>> Others (like fmin_bfgs) strangely converge to a point where the objective
>> is infinite despite the fact that the initial point was not.
>>
>> Do you have any suggestion to fix this problem?
>>
>> regards,
>>
>> Enrico
>>
>>
>>
>>
>> _______________________________________________
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>>
>>
>
>
> --
> Information System Engineer, Ph.D.
> Blog: http://matt.eifelle.com
> LinkedIn: http://www.linkedin.com/in/matthieubrucher
>
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