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

[Enrico Avventi]

forgot the determinant...

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

On Thu, Sep 16, 2010 at 9:57 AM, Enrico Avventi <eavventi at yahoo.it> wrote:

> 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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>>
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