Flexible CGLS for box-constrained linear least squares problems

This paper introduces a new efficient algorithm to approximate a solution of linear least squares problems subject to box constraints. Starting from an equivalent reformulation of the associated KKT conditions as a nonlinear system of equations, the new approach formulates a fixed-point iteration scheme that involves the solution of an adaptively preconditioned linear system, which is handled by flexible CGLS. The resulting method is dubbed 'box-FCGLS'. Box-FCGLS is applied to solve large-scale linear inverse problems arising in imaging applications, where box constraints encode prior information about the solution. The results of extensive numerical testings show the performance of box-FCGLS that, when compared to accelerated gradient-based optimization schemes for box-constrained least squares problems, efficiently delivers results of equal or better quality.