[SciPy-User] optimization with ill conditioned Hessian (josef.pktd at gmail.com)

[josef.pktd at gmail.com]

On Sat, Oct 19, 2013 at 5:09 PM, federico vaggi
<vaggi.federico at gmail.com> wrote:
> Hey Josef,
>
> If the problem you are dealing with is some kind of least square problem,
> you might find this paper helpful:
>
> http://arxiv.org/abs/1201.5885

Thanks for the link.

My problem has a quadratic form but it cannot be rewritten as a least
squares problem, at least not in it's general form.
That's the reason I'm using the general optimizers, mainly fmin and fmin_bfgs.

Josef

>
> Federico
>
>>
>> Message: 1
>> Date: Fri, 18 Oct 2013 22:16:28 -0400
>> From: josef.pktd at gmail.com
>> Subject: [SciPy-User] optimization with ill conditioned Hessian
>> To: SciPy Users List <scipy-user at scipy.org>
>> Message-ID:
>>
>> <CAMMTP+AVZbKmuA60K0dMnWN0nWzKmX1Sg4U5bd1zxM2UwHM1aQ at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> Does scipy have another optimizer besides fmin (Nelder-Mead) that is
>> robust to near-singular, high condition number Hessian?
>>
>> fmin_bfgs goes into neverland, values become huge until I get some
>> nans in my calculations.
>>
>> What would be nice is an optimizer that uses derivatives, but
>> regularizes, forces Hessian or equivalent to be positive definite.
>>
>>
>> Background
>> I'm trying to replicate a textbook example that has data and matrix
>> inverses that are "not nice". fmin (Nelder-Mead) is getting pretty
>> close to the Stata numbers. However fmin_bfgs has been my preferred
>> default optimizer for some time.
>>
>> Aside:
>> It looks like it's a good test case to make my linear algebra more robust.
>> np.linalg.pinv(x.T.dot(x)) doesn't seem to be robust enough for this case.
>> And no idea why a textbook would use an example like that.
>> And no idea if Stata doesn't just make up the numbers.
>>
>> Thanks,
>>
>> Josef
>>
>
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