On iterative algorithms
		      for linear least squares problems
			    with bound constraints

		  M. Bierlaire, Ph.L. Toint and D. Tuyttens

				 Report 89/05

Keywords : Linear least squares, statistical regression, bound constraints,
           iterative methods, active sets, preconditioning, 
           numerical experiments.

Abstract :

     Three new iterative methods for the solution of the linear least
     squares problem with bound constraints are presented and their
     performance analyzed.  The first is a modification of a method
     proposed by Lotstedt, while the two others are characterized by
     a technique allowing for fast active set changes resulting in
     noticeable improvements on the speed at which constraints active
     at the solution are identified.  The numerical efficiency of
     these  algorithms is experimentally studied, with
     particular emphasis on dependence of the starting point choice
     and  the use of preconditioning for ill-conditioned problems.