[SciPy-User] Bounded Linear Least-Squares

[josef.pktd at gmail.com]

On Wed, Apr 20, 2011 at 2:22 PM, Daniel Lepage <dplepage at gmail.com> wrote:
> On Wed, Apr 20, 2011 at 10:54 AM,  <josef.pktd at gmail.com> wrote:
>> On Wed, Apr 20, 2011 at 10:39 AM, Daniel Lepage <dplepage at gmail.com> wrote:
>>> Hi all,
>>>    Does scipy have a function analogous to Matlab's lsqlin? I need to
>>> solve two problems of the form Ax = b, one subject to the constraint
>>> that 0 <= x, and one subject to 0 <= x <= 1. The first case is handled
>>> by scipy.optimize.nnls, but it doesn't support the second. I know that
>>> scipy.optimize includes several constrained optimization routines, but
>>> AFAICT they're all aimed at minimizing arbitrary functions, and as
>>> such I'd expect them to be far slower than an actual linear solver. Is
>>> there such a constrained linear solver in scipy (or numpy, or
>>> scikits.*, etc.)?
>>>
>>> Even better would be a constrained matrix factorization routine, i.e.
>>> that solves AX = B for X with A, X and B all being matrices, subject
>>> to 0 <= X <= 1, but obviously you can construct the latter from the
>>> former, so the former would suffice.
>>
>> I don't know anything that would solve this directly, but I think that
>>
>> scipy.optimize.fmin_slsqp
>>
>> should work well in this case.
>
> It will work, but more slowly than a linear solver because it doesn't
> assume the function to be linear. To even hope to get comparable
> speeds, I'd need to enter the derivatives of my system by hand, which
> is possible but a pain, and even then I expect it will take longer.
>
> Fortunately, I figured out how to restructure my particular problem so
> that I only need nonnegativity, so I'll just use nnls.

Since it's just a linear error function (quadratic objective
function), the derivatives should be easy.

I was just hoping you figure out a recipe example for this since I
also have applications for this case and haven't looked at it yet.

 :)

Josef

>
> Thanks,
> Dan Lepage
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