🚀 go-pugleaf

In article <l9jcdhINNp98@roundup.crhc.uiuc.edu>, hougen@uirvlh.csl.uiuc.edu (Darrell Roy Hougen) writes:
> I would like to find some code, preferably free and preferably in C,
> that solves the general problem of linear least squares with
> linear inequality constraints.  
>

The book "Solving Least Squares Problems"  by C.L. Lawson & R.J. Hanson, 
(1974), Prentice-Hall, explains (chap. 23) how to do linear least squares
inequality contraints (LSI) (mixed with equality):

	minimize ||Ex-f|| subject to Gx>=h

where E, G are matrices, f,h vectors, and x the unknown coefficient vector. 
Equalities constraints are equivalent to two inequalities, x>=y and y>=x, and
unconstrained variables can be set smaller than a large positive number.  
LSI problems can be reduced to least distance problems (LDP):

	minimize ||x|| subject to Gx >= h

LDP problems can be reduced to non-negative least squares (NNLS):

	minimize ||Ex-f|| subject to x>=0

This book provides Fortran code for LDP and NNLS.  Having used the NNLS
algorithm extensively, I have found it robust and efficient.  NNLS can be seen
as a generalization of linear programming since when no solution  exists, NNLS
provides the nearest one, instead of nothing.

> ...
> 
> Thanks in advance.
> 
> Darrell

If anybody knows a more recent general reference about non-negative least
squares,  I would be interested to know about. 

	Daniel Pfenniger