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

[Enrico Avventi]

sure, no problem. the objective function is

f(\Lambda) = trace(\Sigma \Lambda) -  \int_\Pi \log [G(z) \Lambda G(z^-1)']
z^-1 dz

where \Sigma and \Lambda are hermitian matrices, G(z) is complex matrix
valued and analytic inside the unit disc and the integration is along the
unit circle. the function is only defined when G(z) \Lambda G(z^-1)' is
positive definite in the unit circle and tends to infinity when approaching
a value of \Lambda that makes it losing rank.
in some special cases you can then substitute w.l.o.g \lambda with some
linear M(x) where x is a real vector in order to obtain a problem of the
form that i was talking about.

On Wed, Sep 15, 2010 at 10:16 PM, Sebastian Walter <
sebastian.walter at gmail.com> wrote:

> well, good luck then.
>
> I'm still curious what the objective and constraint functions of your
> original problem are.
> Would  it be possible to post it here?
>
>
> On Wed, Sep 15, 2010 at 10:05 PM, Enrico Avventi <eavventi at yahoo.it>wrote:
>
>> i'm aware of SDP solvers but they handle only linear objective functions
>> AFAIK.
>> and the costraints are not the problem. it is just that the function is
>> not defined everywhere.
>> i will experiment by changing the line search methods as i think they are
>> the only
>> part of the methods that needs to be aware of the domain.
>>
>> thanx for the help, i will post my eventual findings.
>>
>> On Wed, Sep 15, 2010 at 6:48 PM, Jason Rennie <jrennie at gmail.com> wrote:
>>
>>> On Tue, Sep 14, 2010 at 9:55 AM, enrico avventi <eavventi at yahoo.it>wrote:
>>>
>>>>  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.
>>>
>>>
>>> IIUC, CG requires that the function is smooth, so you can't use CG for
>>> your problem.  I.e. there's nothing wrong with fmin_cg.  You really need a
>>> semidefinite programming solver, such as yalmip or sedumi.  My experience
>>> from ~5 years ago is that SDP solvers only work on relatively small problems
>>> (1000s of variables).
>>>
>>> http://en.wikipedia.org/wiki/Semidefinite_programming
>>>
>>> Jason
>>>
>>> --
>>> Jason Rennie
>>> Research Scientist, ITA Software
>>> 617-714-2645
>>> http://www.itasoftware.com/
>>>
>>>
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>>>
>>
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