The active-set method for nonnegative regularization of linear ill-posed problems

In this work, we analyze the behavior of the active-set method for the nonnegative regularization of discrete ill-posed problems. In many applications, the solution of a linear ill-posed problem is known to be nonnegative. Standard Tikhonov regularization often provides an approximated solution with negative entries. We apply the active-set method to find a nonnegative approximate solution of the linear system starting from the Tikhonov regularized one. Our numerical experiments show that the active-set method is effective in reducing the oscillations in the Tikhonov regularized solution and in providing a nonnegative regularized solution of the original linear system.