[SciPy-User] Bounded Linear Least-Squares

[Daniel Lepage]

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.

Thanks,
Dan Lepage