For the solution of large sparse box constrained least squares problems (BLS), a new class of iterative methods is proposed by utilizing the modulus transformation, which converts the solution of the BLS into a sequence of unconstrained least squares problems. Efficient Krylov subspace methods with suitable preconditioners are applied to solve the inner unconstrained least squares problems at each outer iteration. In addition, the method can be further enhanced by incorporating the active set strategy, which contains two stages where the first stage solves the reduced unconstrained least squares problems only on the inactive variables, and projects the solution into the feasible region. We also analyze the convergence of the method including the choice of the parameter. Numerical experiments show the efficiency of the proposed methods in comparison to the gradient projection methods, the Newton like methods and the interior point methods.

This is joint work with Dr. Ning Zheng and Prof. Jun-Feng Yin