LLSP

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Linear Least Squares Problems (LLSP)
\frac{1}{2} \mathbf{\| C x - d \|^2} + \frac{1}{2} \mathbf{\mu \| x - \widehat{x} \|^2 \rightarrow min}
subjected to
\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}
\mathbf{A x} \le \mathbf{b}
\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}


Notes:

  • damp factor  \mathbf{\mu} and value  \mathbf{\widehat{x}} are handled by OpenOpt as "damp" and upper-case "X" variables
  • If damp is provided (by user) but vector X is not, then X is filled by zeros.

LLSP solvers connected to OpenOpt:

Solver License Optional data that can be handled Sparsity handling Made by Info
(since v 0.28) lsqr GPL  \mathbf{\mu} (damp) Yes (use scipy.sparse or FuncDesigner AD) Michael P. Friedlander (University of British Columbia), Dominique Orban (Ecole Polytechnique de Montreal) Parameters: atol (1e-9), btol(1e-9), conlim ('autoselect', 1e8 for LLSP and 1e12 for SLE). Since the solver is very small (about 300 lines of code) for to simplify its installation it is spread with OpenOpt, so you should remove it if you can't use GPL soft. I have asked its developers about its license and some other issues, but seems like their emails are deprecated.
(since v. 0.38) pymls BSD lb,ub No Till Stensitzki, based directly on code from qcat from Ola Harkegard (http://research.harkegard.se/) Requires SciPy installed; seems like it badly handles problems with bounds over +/-10^9. For infinity bounds +/-10^9 are substituted instead (elseware nan is returned).
lapack_dgelss BSD None  ? Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University double precision, requires SciPy
lapack_sgelss BSD None  ? Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University single precision, requires SciPy
bvls BSD lb, ub No Robert L. Parker rlparker(at)ucsd.edu, Philip B. Stark stark(at)stat.berkeley.edu Installation: download bvls.f (this one is a little bit modified for f2py using), type in terminal "f2py -c -m bvls bvls.f" (it requires already installed: 1) numpy; 2) fortran compiler;) and put bvls.so into a directory from PYTHONPATH (for example, /usr/bin/python2.5/site-packages).
converter to nlp those ones that can be handled by the NLP solver involved mb depends on the solver involved Dmitrey Example: r = p.solve('nlp:ralg', plot=1). Recommended solvers: scipy_slsqp (constrained), scipy_ncg (unconstrained)


See also:

SLE (System of linear equations)
Retrieved from "http://openopt.org/LLSP"
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