  We present the Residual Quadratic Programming Active-Set Subspace (ResQPASS)
method that solves large-scale linear least-squares problems with bound
constraints on the variables. The problem is solved by creating a series of
small problems of increasing size by projecting on the basis of residuals. Each
projected problem is solved by the active-set method for convex quadratic
programming, warm-started with a working set and solution of the previous
problem. The method coincides with conjugate gradients (CG) or, equivalently,
LSQR applied to the normal equations when none of the constraints is active.
When only a few constraints are active the method converges, after a few
initial iterations, like the CG and LSQR. An analysis links the convergence to
an asymptotic Krylov subspace. We also present an efficient implementation
where QR factorizations of the projected are updated over the inner iterations
and Cholesky over the outer iterations.
