Introduction
BCLS is a software package for solving bound-constrained least-squares problems of the form
![\[ \begin{array}{ll} \displaystyle\mathop{\hbox{minimize}}_x & \frac12\|Ax-b\|_2^2 + \mu\frac12\|x\|_2^2 + c^T x \\ \hbox{subject to} & \ell \le x \le u. \end{array} \]](form_2.png)
The m-by-n matrix 
can be any shape. The regularization and linear terms are optional. The vectors 
and 
define upper and lower bounds on the variables 
. Free and fixed variables are easily accomodated by setting corresponding components of and to be 
and 
, or by setting them equal to each other.
BCLS implements a two-metric projected-descent method. At each iteration, a search direction is computed that is a combination of a Newton and a scaled steepest-descent step.
Some notable features of the implementation:
- The matrix is used only as an operator. The user needs only to provide a routine to compute the matrix-vector produts
and 
- The algorithm can take advantage of good starting points, and is capable of making very large changes to the "active-set" at each iteration.
- The normal equations are never formed.
- The user may provide perconditioners in order to accelerate the solution of the subproblems.
BCLS is written in ISO C and should compile on most systems (thanks for the Autoconf/Automake tools). No additional software is required, though there should be a significant speedup if it is compiled against a tuned BLAS library such as ATLAS. It has been tested using GCC on GNU/Linux, Mac OS X, and Windows XP (under MinGW).
License
BCLS is open-source software released under the L-GPL license. Feel free to use it in any way you wish. If you find it at all useful, I'd like to hear from you, please send email.