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Re: GSoC 2015: Optimization Package: Non-linear and constrained least sq
From: |
Olaf Till |
Subject: |
Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin |
Date: |
Wed, 25 Feb 2015 12:02:58 +0100 |
User-agent: |
Mutt/1.5.21 (2010-09-15) |
On Tue, Feb 24, 2015 at 10:03:15PM +0000, Asma Afzal wrote:
> <snip>
> [2] just explains the unconstrained case (which I was referring to
> for the basic understanding of how the LM algorithm works), but the
> non-linear constraints are considered in the levmar.c library [3].
>
> --start quote
>
> To deal with linear equation constraints, levmar employs variable
> elimination based on QR factorization, as described in ch. 15 of the
> book Numerical Optimization by Nocedal and Wright. For the
> box-constrained case, levmar implements the algorithm proposed by C.
> Kanzow, N. Yamashita and M. Fukushima, Levenberg-Marquardt methods
> for constrained nonlinear equations with strong local convergence
> properties, Journal of Computational and Applied Mathematics 172,
> 2004, pp. 375-397
>
> --end quote
Variable elimination should not be applicable if general non-linear
constraints are also present (one doesn't even know which variables
are referenced by the user function for general constraints). BTW if
variable elimination is applied (if applicable), it should be done
already in the frontend (the function providing the user interface),
so that it is available for all backend algorithms; it should be done
in the same way in the frontends for scalar optimization, not only in
the curve-fitting frontends. OTOH I'd think that the available
projection algorithms can trace linear equality constraints quite
efficiently, limiting the usefulness of variable elimination.
And box constraints are linear, or is something different meant here?
So no non-linear constraints ... (?)
> <snip>
> 3) Rewriting levmar C library into m-code for Octave? Or is there a
> C library used by the optimization package that would benefit from
> porting into m-code?
I meant the former. But as I said, I'm not sure.
> What would you suggest as the most suitable contribution as part of GSoC?
I'm not sure at present.
- For my (current) opinion on providing 'lsqnonlin' et al. see my
answer to Nir.
- Having a further algorithm for residual minimization (i.e. curve
fitting) would be good, but actually I'd prefer an algorithm
featuring also non-linear constraints, preferably an algorithm which
honours the constraints only in the result (since the current
algorithm honours them throughout optimization, which might not
always be the best). (I havn't searched for such an algorithm as
yet.) The potential advantage of the levmar.c algorithm is probably
very limited.
Olaf
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- GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, AsmaA, 2015/02/23
- Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, Olaf Till, 2015/02/24
- Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, Nir Krakauer, 2015/02/24
- Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, Olaf Till, 2015/02/24
- Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, Nir Krakauer, 2015/02/24
- Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, Olaf Till, 2015/02/25
- Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, Julien Bect, 2015/02/25
Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin, Asma Afzal, 2015/02/24
- Re: GSoC 2015: Optimization Package: Non-linear and constrained least squares lsqcurvefit, lsqlin, lsqnonlin,
Olaf Till <=